[Graybeard]

Originally Posted by WIKI It has been over ten years since M-Theory was first proposed by Ed Witten. When Witten named M-theory, he did not specify what the "M" stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe.

How does it look over a decade further on!

The following 5 posts are taken from a lecture delivered at the Kavli Institute for Theoritical Physics in January-1998 by Ed Witten on what appears to be a whiteboard, 10 years ago to the Month. The reason that I have put them into 5 posts is for coherant perusal, as they occupy over 50 web pages here. Nothing has been changed ... There is no Maths and they are very easy to understand ... So if you would like to know a little about String Theory's place in Science... this will explain it ... greg

Duality, Spacetime and Quantum Mechanics

Intro: (January 1998)
In the last few years, physicists have learned that the different string theories discovered and studied in different ways are limiting cases of a single, more powerful theory, known as M theory. "M" stands for magic, mystery, or matrix, according to taste. Some of these developments will be explained in this lecture.

Edward Witten, professor of physics at the Institute for Advanced Study in Princeton, N.J., is arguably the premier theoretical physicist of our time. Renowned for his many contributions to particle physics and string theory, Witten has almost single-handedly constructed a new branch of mathematical physics For his achievements, he has been awarded mathematics' highest prize, the 1990 Fields Medal. A member of the National Academy of Sciences, he is a recipient of a MacArthur Prize, the Dirac Medal, and many other honors.

[Graybeard]

Written and Illustrated by Ed Witten. (Slides 1 to 10 of 48)

1.. One bit of Physics that most of you have probably seen in high school is the inverse square law of Gravity and Electricity. The force between two charges separated by a distance is (e1 x e2) / r^2

2.. And likewise the forces between two masses is G ((m1 x m2) / r^2). (Slide 2 below.)

That was fine for the first 200 years or so, but just about a century ago the electron was discovered and ever since

3.. Physicists have had to grapple with the singularity of the inverse square law at R = 0 (e1 x e2) / R^2 (Slide 3 above)

4.. This singularity seemed to imply, for instance, that an atom could survive for only about 10^-9 seconds. (Slide 4 below)

This problem, in the case of electricity, was solved in the first half of this century with the development of Quantum Mechanics

5.. The solution is based on the 'Uncertainity Principle' .. everything is a bit fuzzy if expressed in classical terms. (Slide 5 above.) The quantum uncertainity 'smears out' the singularity at R = 0

6.. It turns out though, that quantum uncertainity doesn't solve the problem for Gravity. The analogy between Gravity and Electricity is quite as close as the Inverse Square Laws G((m1 x m2) / R^2) or (e1 xe2) / R^2 suggest ....

7.. In fact, since 1915, Gravity is really described by Einstein's Theory of General Relativity, whose non-linear mathematics is such that quantum uncertainity alone cannot solve the problems of the inverse square law.

8.. This problem is at the center of physics, since in fact physics in our time is based on 2 great theories. Quantum Mechanics of Atoms and Sub-Atomic particles (small) and General Relativity which equals Einstein's Theory of Gravity (large) which are in conflict ---- a conflict which is the modern version of earlier contradictions that led to the upheavals in twentieth century physics .......

9.. This leads us to String Theory. Physicists had the good luck to discover, essentially in the 1970s, that this problem can be overcome in string theory. In string theory roughly speaking one reinterprets an elementary particle not as a point but as a vibrating loop or string. (Slide 9 below)

10.. One of the reasons that this is very rough is that one should include quantum uncertainity on each side. (Slide 10 above) Now one of these strings, just like a violin or piano string, has many different modes of oscillation or harmonics. In the present context one interprets these as different elementary particles.

continues in next post .....

[Graybeard]

Written and Illustrated by Ed Witten. (Slides 11 to 20 of 48)

11.. So a single string describes all at once a huge assortment of different particles. Since one learns to correctly 'quantise' the string and 'compute' the 'spectrum' one finds that one of these particles has just the right properties to be the 'graviton', or quantum of gravitational waves. ---- This is the beginning of the discovery that ....

12.. In contrast to convential quantum field theory, which makes gravity impossible, string theory requires gravity. Other modes of the string look like the photon, electron, muon, quarks, neutrinos, etc. That is, with very simple assumptions, 'everything' fits neatly into a string.

13.. In a way that is uncannily like what we see in nature. For a simple explanation of why string theory turns out to have such nice features ... lets go back to standard quantum theory.

14.. According to Feynman, one calculates the details of physical processes in quantum (field) theory via 'Feynman Diagrams'. (Slide 14 below)

15.. The lines in a feynman diagram represent free propagation of particles. (Slide 15 above) But the vertices. (Slide 15 above) are interaction events where particles branch and rejoin.

16.. There are lots of great things about Quantum Mechanics but its limits. (Slide 16 below)

can be seen here: 1.. There are too many theories, differing by what kind of vertices one allows. 2.. Infinities (which eventually make gravity impossible) come when X = Y = Z = W. (Slide 16 above)

17.. In String theory one replaces the propagating point particle. (Slide 17 below) by a propagating string. Slide 17 below)

18.. So ... (Slide 18 below) The 'vertices' have disappeared, so a) very few theories b) Finite - no trouble with inverse square law. [possibly jump to 22 .. 19, 20, 21 appear to have been added later... greg]

19.. The statement that there are 'very few theories' means, to be precise, that once one understands the motion of a free string. (Slide 19 below) one automatically understands
the interactions, since the pictures look everywhere locally the same. (Slide 19 below)

20.. This contrasts with field theory, where after describing the free motion. (Slide 20 below) one must still describe the interactions or vertices. (Slide 20 below)

continues in next post .......

[Graybeard]

Written and Illustrated by Ed Witten. (Slides 21 to 30 of 48)


21.. When the dust clears there are just 5 string theories, discovered from 1970 -84. Type I, Type IIA, Type IIB, Hetorotic E8E8 and SO/32 which differ by general properties of the strings.... raising an obvious question ....

22.. Reducing this way the number of theories has a fateful consequence . In Standard Physics the 'free motion in spacetime' can be described abstractly and doesn't really contain much information about spacetime.... (Slide 21 below) .... but the interactions depend on knowing exactly where you are. (Slide 21 below)

23.. In string theory that last part is missing so one never learns precisely what the spacetime is .... There is a new source of fuzziness that goes beyond quantum mechanical uncertainity... (Slide 23 below)

24.. Just as Quantum Mechanics puts a bound on how precisely defined can be 'the trajectory of a particle', so String Theory puts a bound on how precisely one can describe 'Spacetime'

26.. In Quantum mechanics. (Slide 26 above) is the basic scale of quantum uncertainity. In String theory, theres a new constant. (Slide 26 above) that plays an analgous role.

27.. String Theory makes three 'general' predictions.

• Gravity
• Gauge Symmetry
• Super Symmetry

and with a knowledge of the vacuum one can hope to learn more.

28.. (rather as standard quantum theory makes one general prediction - antimatter - and specific quantum field theories make more specific predictions ... )

29.. I.. Gravity means here, Einstein's Theory of General Relativity which is automatic in String Theory, while standard quantum field theory makes it impossible. II. Gauge Symmetry is the bread and butter of the standard model of particle physics.

30.. Super Symmetry. Alongside the usual or 'Bose' dimensions of Spacetime. t = time & Space = x,y,z. There would be new, or infintismal quantum or 'Fermi' dimensions.
(Slide 30 below). Predicts new particles, oscillations in the fermi dimensions.

continues in next post .......

[Graybeard]

Written and Illustrated by Ed Witten. (Slides 31 to 40 of 48)

31.. In contrast to Gravity and Gauge Invariance, we don't yet know if SuperSymmetry is true in nature. It is one of the main targets of accelerators, including the former SSC and the future LHC (to operate at CERN, in Geneva around 2005) as well as machines that operate currently.

32.. There are some indirect experimental hints that SuperSymmetry is 'near' in energy. Coupling Constants, Energy Scales. .... if it were found that would be quite a momentous discovery, and certainly a big boost for String Theory.

33.. Bad News ? ... its time to explain why the Cosmological Constant is Zero, and we haven't ! (Slide 33 below)

34.. More 'Cosmically'. We don't really understand what the theory is. (Slide 34 above) You can describe much of Physics by particles or waves, but the waves are more fundamental; only the less fundamental particle view has been generalised in String Theory ....

35.. (Slide 35 below) So 'What is String Theory?'

36.. The problem as I have just posed it has been with us for some years, but the outlook has changed a lot in the last couple of years because of a new understanding of the role of 'duality'.

37.. In its oldest form 'duality' is a symmetry between electric and magnetic fields which holds in vacuum but is spoiled in nature (apparently) by the fact that we see electrons but not magnetic monopoles. (Slide 37 below)

38.. Quantum mechanics actually seems to make duality impossible (because of the role of the vector potential) In the 1870s (possibly means 1970s ??) Olive and Montonen had a remarkable insight about how duality might work in quantum theory.

39.. But it seemed well out of reach to determine if it was really true. That was because of a basic limitation in our abilities in physics; We are generally able to compute what happens only when the charge, e, is much less than one.

40.. Duality, though, exchanges e with 1/e and it is not possible to have both e and 1/e be much less than 1.

continues in next post .......

[Graybeard]

Written and Illustrated by Ed Witten. (Slides 41 to 48 of 48)

41.. To test, or use, duality one has to somehow get beyond the traditional limitation of small e. And thats what happened in the last three years, (this written in 1998) with broad implications for our understanding of Standard Quantum Field Theory and String Theory.

42.. For Standard Quantum Theory we get new insights about traditional problems like 'Quark Confinement'. (Slide 42 previous post) which is related by duality to more standard physics.

43.. For String Theory we have obtained the amazing insight that ... Theres only one Theory .. the six theories discovered and studied in the last 12-25 years (Type I, Type IIA, Type IIB, Hetorotic SO/32, E8xE8, 11 dimensional SUGRA) are different limiting cases of one Theory.

44.. to understand this, we have had to crack the small e barrier, since for small e the barriers are really different. (Slide 44 below)

45.. We have also obtained a rather different view of the basic ingredients of String Theory ... Strings are, in a sense only, at most, the 'First among Equals' and share the stage with objects like 'D-branes' that are related to strings by duality.

46.. A concrete application is to 'Black Holes'. For the first time we have been able to understand the 'quantum states' or 'elementary constituents' of a Black Hole'.

47.. The big question to me, looking ahead, is whether with our new understanding we are finally well placed to answer the Big Question "What is String theory?". If we really understood that I feel sure a lot of things would become clear.

48.. Slide 48 below

Ends .......

[Graybeard]

Well .... 10 years is a long time. Our forum (Roberts) is not that old.

And yet String Theory with its promises and problems is still with us. Despite the growing throng of detractors, informed and uninformed, vociferously predicting its almost certain demise, it remains.

Not only remains, but has not taken, in all that time a mortal wound. It has not furthered its promises, it has not solved its problems, but it has not been extinguished.

What do you think ? Worthy of consideration or not!

cool bananas ... greg

[dipayankar]

Great posts Greg... I however got stuck in e barrier. Can you please explain it in detail?? I am the donkey you see....

Originally Posted by Graybeard Written and Illustrated by Ed Witten. (Slides 41 to 48 of 4 41.. To test, or use, duality one has to somehow get beyond the traditional limitation of small e. And thats what happened in the last three years, (this written in 199 with broad implications for our understanding of Standard Quantum Field Theory and String Theory. 42.. For Standard Quantum Theory we get new insights about traditional problems like 'Quark Confinement'. (Slide 42 previous post) which is related by duality to more standard physics. 43.. For String Theory we have obtained the amazing insight that ... Theres only one Theory .. the six theories discovered and studied in the last 12-25 years (Type I, Type IIA, Type IIB, Hetorotic SO/32, E8xE8, 11 dimensional SUGRA) are different limiting cases of one Theory. 44.. to understand this, we have had to crack the small e barrier, since for small e the barriers are really different. (Slide 44 below) 45.. We have also obtained a rather different view of the basic ingredients of String Theory ... Strings are, in a sense only, at most, the 'First among Equals' and share the stage with objects like 'D-branes' that are related to strings by duality. 46.. A concrete application is to 'Black Holes'. For the first time we have been able to understand the 'quantum states' or 'elementary constituents' of a Black Hole'. 47.. The big question to me, looking ahead, is whether with our new understanding we are finally well placed to answer the Big Question "What is String theory?". If we really understood that I feel sure a lot of things would become clear. 48.. Slide 48 below Ends .......

[Graybeard]

Dip .... I'm not sure and would only be guessing. However I see part of the problem

From 1 .. 'e' appears to be the charge in the inverse square law of Electricity. The force between two charges separated by a distance is (e1 x e2) / r^2. eg: the further apart they are (r = distance) the less the force acting between them because r^2 is the divisor ...

From 39 .... That was because of a basic limitation in our abilities in physics; We are generally able to compute what happens only when the charge, e, is much less than one. (What this means I don't know)

From 40 ...... Duality, though, exchanges e with 1/e and it is not possible to have both e and 1/e be much less than 1.

The problem here is that duality of a particle describes its particle/wave function. But in String Theory duality describes the uncertainity of Spacetime (see From 37 ... and externally the 'monopole' problem)

Altho I don't understand the reasoning, e needs to be less, much less than 1. But with String Theory duality both 'e' and '1/e' are used and they both need to be less than 1.

If 'e' is less than 1, then 1/e will be greater than 1. How they solved this in the 3 years prior to 1998 Phuck knows ..

Everything I am saying here may be an absolute load of crap, so don't take it too seriously .. LOL

I will ask Dave if he can have a go at explaining it for us ....

cool bananas ... greg

[dleviwing]

Originally Posted by Graybeard Everything I am saying here may be an absolute load of crap, so don't take it too seriously .. LOL

This is probably the most accurate statement in the entire thread; it's not what you are saying though, it’s what the string-theorists are attempting to have you swallow.

This is where the gauge theories break down big time and when the scientist have their heads too far up their math. We cannot allow the math to dictate what is real but must first know the properties of what is real in order to know the limits to place on the math.

String theory provides a few extra decimal place of accuracy to gravitational effects.
QM works well with the finite small.
Relativity works well with the cosmologically large.
WHY? Answer that and you will understand the limits of each and just dismiss string theory all together. Understand what creates “MASS” and you will have the basic key to understanding the physical portion of the TOE; then you can concentrate on “emergence”.

QM is the key to understanding what initiates gravity; you just need to sort it out from all the add-on bull-crap. Go back to the original philosophies of Planck’s QM and stop listening to the exaggerated probability and uncertainty BS; that's just methodology.

BTW: (e1 x e2)/r^2 is only valid for forces that are independent; electrons with the same quantum qualities will simply stick together.