The Superstring theory is a theory in process. It is now more than 30 years since it first began. Scientists have since learned a lot more about it, developed and worked out a lot more details about how the various shapes of the strings may affect their peculiar characteristics, and tried out a huge number of calculations to make them square with the results of what other scientists have learned by what has been called "The Standard Model" and explained quite a bit about certain anomalies which scientists using the equations of "the Standard Model" were unable to account for and increased our understanding of how strings would behave under different contexts. But they feel that they still have not gone to the core of it. They still have not yet found a principle deep enough to account for every phenomena they hope to be able to explain in the same way that "special relativity" may be explained by factoring in the principle of invariability of speed of light and "general relativity" by the principle of equivalence and "quantum theory" by the principle of uncertainty. The furthest string theorists have gone in the direction of developing that kind of theory of force, matter and cosmomology is one called the M-Theory.
According to Brian Greene (The Elegant Universe1999 & The Fabric of the Cosmos 2004), the failure of string theorists to explain many things may be due to the fact that the "old string theory" developed by fits and starts and did not have a "grand, overarching vision." They tinkered with this and that, and made use of accidental discoveries in specific areas of scientific researches and mathematical theories and then tried to work out their implications by applying it to widely different quantum contexts. Up until 1995, string theorists have found that there are a total of 5 distinct versions of the string theory called respectively Type I (involving both closed strings with circular ends and open strings with two loose ends) , Type IIA, Type IIB ( where strings interact through pinching a circular string into two smaller strings rather like what happens during the mitosis of a cell) , Heterotic-O ( which accomodates symmetry groups called 0(32)) and Heterotic-E ( which accomodates symmetry groups E(8) x E (8) ) both the latter of which are large enough to accomodate what has been called the Grand Unification Theory (GUT). Each of such string theories requires 10 space dimensions and each are compatible with the known characteristics of different families of sub-atomic particles as currently understood.
Of the 5 theories, the most realistic is that of the heterotic-string as worked out by David Gross, Emil Martinee, Ryan Rohm and Jeffrey Harvey of Princeton University. This hetero-string is based on closed strings and is able to accommodate the symmetry of the Standard Model because the symmetry group E(8) x E(8) can be broken down into E(8) and then E(6) symmetry which in turn may include the SU (3) x SU (2) x U(1) symmetry of the Standard Model.
Then in 1995, Edward Witten, based on the previous work of Chris Hull, Paul Townsend, Ashoke Sen, Michael Duff, John Schwarz and others, was able to show that the five existing string theories can be considered as just 5 different ways of mathematically analyzing a single theory which he calls M-theory (M standing for master, mother, magic, mystery, matrix,, even membrane or all of them) and including time, 11 dimensions. Just as Kaluza found that a universe with 5 spacetime dimensions provided a framework for unifying electro-magneticism and gravity, and string theorists found that a universe with 10 spacetime dimensions provided a framework for unifying quantum mechanics and general relativity, Edward Witten found that a universe with 11 spacetime dimensions provided a framework for unifying all string theories! What's more, string theorists now find that the string theory is not just a theory about strings! It may also include something called a membrane, abbreviated into the word "brane", rather like a thin rubber sheet on the surface of a balloon. The reason is that previously string theory researchers found that all the conditions for agreeing with the observed findings of physics could be met by a one dimensional string. But later, they found that whilst their theory worked fairly well if they stuck to a string with just one dimension, it seemed impossible to proceed if the fundamental ingredients has 2 or more dimensions because the number of symmetries respected by the equations peaks enormously for one-dimensional objects like a string. They found that thereafter such suitability dropped off very sharply after the first dimension (this had to do with the number of symmetries they can adequately handle: such that the relevant equations must change whenever the observer zooms in and zooms out, suddenly and arbitrarily whilst observing the motion of a string, if they wish not to affect the "resolution" or clarity or accuracy of his observation). The net result of this is that the higher the energy level, the more inaccurate the calculations become.
Now according to this new M-theory, which is the furthest development of what started out as string theory, they had to posit the existence of a membrane. This newly posited membrane may have 2-branes, 3-branes or p-branes ( or p spatial dimensions but p must be any integral number so long as it is less than 10) . In addition, they think that strings are only one of the ingredients in string theory, not the only one! The super-membrane can have two or more dimensions because it represents a surface whereas the string has only one dimension that defines its length. Surprisingly, they found that two types of membranes viz. the 2-brane and the 5 brane are self-consistent with 11 spacetime dimensions! Of course, the 10th space dimension has not been previously detected. The reason might be that it involved dimensions which are simply so ultra-small. Whatever the reason might have been, their calculations have shown that all p-branes are significantly heavier than strings. We know that because of the equivalence of mass to energy under the theory of relavity: the heavier they are, the more force will be required to produce them. At the extreme energies required to produce p-branes , the previous approximate equations are shown to lack the kind of precision which will be sufficient to expose the lurking presence of such branes!However, this does not mean that all the previous calculations and equations based on the old string theory are thereby invalidated. It only means that they are now more refined and less approximate!
Witten and Paul Townsend of Cambridge University made a remarkable discovery in 1994. They found that the old 10 dimensional string theory can be considered an "approximation" of a higher, mysterious 11-dimensional theory (of unknown origin) but that if we were to reframe our mind into that of a "membrane like" theory of a world of 11 dimensions and then curl up one dimension, it would become the old 10-dimensional type IIa string theory. In addition, the supergravity theory (which only contains two particles of zero mass ie. the graviton and the gravitino) may thus be considered a subset of the M-theory! In other words, we can explain the existence of supergravity if we assume a tiny portion of M-theory (which as a whole deals with an infinite number of particles with different masses) and restrict ourselves to just that portion of its theory about massless particles, then it would become the old supergravity theory. In the same manner, if we take a sphere in 11 dimensions, curl up one dimension, the sphere will "collapse" and its equator become a closed string, then it will become a "slice of a membrane" in 11 dimensions. We may then consider the 11th dimension as being curled into a small circle. Thus the M-theory nicely ties up all 10 and 11 dimension strings and membranes.
M-theory thus have the largest set of symmetries known to physics. Not only that, all 5 string theories are "dual" to each other and may share certain family resemblance in more or less the same way that low charge electricity may be equivalent to or resemble high-charge magneticism. Thus whilst type I string theory is based on closed and open strings that can interact in 5 different ways with string splitting and joining and S0(32) string is based entirely on closed strings that have one way of interacting and will undergo splitting, Type I theory is defined in 10-dimensional space but S0(32) vibration is defined in 26 dimensional space, IF however we allow the strength of the interaction to increase, type I strings will change into S0(32) heterostrings! Perhaps this is why so many physicists are so engrossed and enchanted by the M-theory and the string theories. There is such symmetry and elegance! Everything known about particles and gravity seems to tie in together so nicely!
There are some indications that the mass of a higher dimensional brane can be on par with the lowest mass string vibrational patterns and that if so, they may have a significant effect on the resulting physics, according to Greene. M-theorists now posit that the universe in which we find ourselves may be nothing but an enormous brane! It may well be that the additional 10th space dimension required by string theory may hug so closely to the surface of the universe that but for the minor discrepancies which the string theorists have discovered in their calculations when they try to figure out the "missing" energies in the relevant equations, it might never have been "discovered" because of their extremely small size! Another reason might be that the higher dimension are so tightly wound up by the tremendous force of the relevant strings that they never have the chance to be unravelled and to expand into a size measurable by our current instruments of measurements. Whatever might be the beauty of the M-theory, the fact remains that no one has yet found firm evidence of the existence of the additional 6 or 7 dimensions posited by string theory and M-theory because their discovery will require measurements of distances smaller than those permitted by any instruments of our present technology and also the production of energies which our current particle accelerator are capable of by many order of magnitudes! So string theory and M-theory remain mathematically possible theories only! They may or may not have any relation to what we normally regard as physical "reality".
18 March
What Makes the Superstring Super?
I have often wondered why some scientists call the strings in the string theory "superstrings". Now I think I know, thanks to Brian Greene. He explains that in chapter seven of his classic The Elegant Universe I mentioned in one of my earlier blogs. That chapter is headed "The Super in Superstrings".
It appears that that adjective indicating the superlative is related to one particular feature that scientists often find in nature and which may sometimes serve as his guide in the search to uncover Nature's secret. That feature is called "symmetry". Einstein was reported to have said that he would feel sorry for God if the Almighty were to pass over his General Theory of Relativity because it was so simple, condensed, powerful and hence elegant and beautiful. Scientists often follow their hunch in pursuing a particular line in their research simply because the formula which they hope to form the basis of their theory appears to them so elegant and beautiful. Of course, beauty is no guarantee of correctness. But in practice, they often do. And in physics, symmetry often seem a good bet. String theory seems to embody a "super symmetry" in the sense that it can be applied in the explanatory context of so many different kinds of forces.
In physics, scientists expect nature to behave in a "regular" and hence predictable manner. The laws of physics are supposed to be universal: they will apply no matter where and when they are tested. They are supposed to apply in all kinds of places and all points in time! Ideally, they should be true everywhere and at all times, in all parts of the universe, in all macrocosms and as well as in all microcosms.. Nature is expected to display "symmetries"! The laws of gravity apply not on earth but on the moon and on the sun and in all the galaxies. The laws of physics treat all observers everywhere alike! Even though Einsein has taught us that we must take into account the "relative" speed or acceleration of the celestial body from which the relevant observer makes his observation, the same physical laws still apply. The applicability of the laws of physics does not depend on the "angle" of observation.
The laws of physics treat all possible "orientation" on an equal footing. Even if you were to rotate all your experimental equipment and repeat the same experiment, the results will be the same. This is called rotational symmetry. However, in 1925, George Uhlenbeck and Samuel Goudsmit found out something more. They found that a number of properties of light emitted and absorbed by atom could only be explained by supposing a special property of electrons called "spin" (in more or less the same the same way that the earth rotates both around an unchanging axis and at the same time revolves around some other object in space like the sun). In the case of the electron, there is a "spin" around the nucleus of the atom, in a specific orbit. What they found is that all the electrons in the universe spins at one fixed and never changing rate! Such a property is regarded as an "intrinsic"property of an electron just like its mass or its electric charge. Since then, scientists have found that this property is not just peculiar to the electron alone. All other matter particles and also their partner anti-particles are found to behave in exactly the same way: they all have a spin equal to that of the electron! Hence there is now an additional symmetry in Nature. In the technical language of the scientists, they say that all "matter particles" have a "spin-1/2", where the value of 1/2 is roughly a measure of how quickly the particle rotates. But the "non-gravitional force particles" like photons, weak guage bosons and gluons have an intrinsic spin whose value is twice that of the "matter particles": they have a spin of 1 and that the graviton has a spin of 2. Even in 1974, Scherk and Schwarz have already predicted from their string theory that one of the the strings would have a spin of two and is massless. That appears to fit in perfectly with what is required of the graviton! This additional symmetry is now called by scientists "super-symmetry". It is "super" because it "transcends" or goes beyond the "classical" symmetry of rotation in time, in spatial location, in angular orientation, in velocity of motion. It is associated with a change in observational vantage point in the context of "quantum mechanical extension of space and time".
If the universe is really "super-symmetric" then the particles of Nature must come in pairs ( called "superpartners) whose respective spins differ by half a unit! Since the matter particles or strings ( tiny vibrating loops) have spins of 1/2 while some of the messenger particles have a spin of 1, then supersymmetry suggests a "partnering" of matter particles and force particles! If so, we will have a theory which unifies all forces, including gravity. Supersymmetry is the only symmetry that interchanges all the sub-atomic particles known to physics. It classifies these particles by their spins: thus photon which mediates between electro-magnetic force has spin 1; the weak and strong nuclear forces, mediated by W-bosons and gluons, also have spin 1; the graviton has spin 2 (all particles having integral spin being called generically "bosons") whilst particles of matter have half spins and are generically called fermions (including the electron, the neutrino and the quarks). Because in string theory, all the sub-atomic particles have a partner, each fermion is paired with a boson. Because all subatomic particles are either fermions or bosons, supersymmetrical theory has the potential for unifying all the known sub-atomic particles into one simple symmetry. It is a symmetry which include all the particles of the entire universe!
However, in the mid-1970s theoretical scientists found that none of the known particles like electrons, neutrinos, up/down quarks, to/bottom quarks, charm quarks, strange quarks, taus, gluons, photons, bosons, gravitons could be superpartners of one another and further calculations show that if the universe were to incorporate supersymmetry, then every known particle must have a superpartner particle (as yet undiscovered) whose spin should be half a unit less than the spin of the known superpartner particles i.e. the known particle's (e.g. an electron) superpartners should have a "spin-0" . They call such a superpartner particle of an electron a "selectron" ( abbreviation of supersymettric electron) . Likewise the superpartner of a neutrino would be called "sneutrino" and a superpartner of a quark would be called "squark" and for force particles like photons, their corresponding superpartners would be called "photinos", for gluons, "gluinos" and for W-bosons, "winos" and for Z bosons "zinos" etc. If so, does that mean that instead of making physics simpler and more elegant, string theorist makes it even more clumsy and cumbersome and we must abandon string theory? No, according to Greene! For three reasons. Nature does not necessarily have to follow all possible mathematical principles and symmetries. Second, to make Nature supersymmetric, we can fine tune Nature's values to a special value to fit with the standard model. However, if we were to adopt supersymmetry we may have cancellations. Thus bosons, whose spin is a whole number and fermions whose spin is half of a whole(odd) number) tend to give cancelling quantum-mechanical contributions such that when the quantum jitters of a boson are positive, those of a fermion tend to be negative and vice versa. As supersymmetry requires that bosons and fermions occur in pairs, substantial cancellations are bound to occur so that the quantum frenzy is considerably reduced and we no longer have to rely on the extremely delicate values required by the standard model. Thus while according to the standard model, at extremely high temperatures, e.g at 1028 Kelvin when the universe was about 10-39 of a second old, the strength of the three non-gravtional forces ie. strong and weak nuclear forces and the electromagnetic forces may all merge together into one grand homogenous force plasma, when the size of the universe was about is 10-29 of a centimeter or just
about about 10,000 times larger than the Planck length. Georgi, Quinn and Weinberg have argued that the reason why we now find that these three forces are so different is because of the different effect of the haze of microscopic quantum activity on each such force.
In 1973, Gross and Frank Wilczek and also David Politzer argued that the quantum cloud of particle eruptions and anihilations "amplifies" the strengths of the strong and weak nuclear force. If so, the shorter the distance between the particles, the less amplifications there will be. In 1991, Ugo Amaldi of CERN, Wim de Boer and Herman Furstenau of Germany recalculated the Georgi, Quinn & Weinberg extrapolations and found that the value of the three forces almost but still not quite agree at tiny distances at extremely high temperatures but that once supersymmetry is incorporated, the tiny discrepancies in the calculations disappears! The reason is that the superpartner particles contribute additional quantum fluctuations which just adds sufficient force to make the three forces converge with each other.
Superstring theory, as modified by the works of Ferdinand Gliozzi, David Olive, Andrew Neveu is the only theory we now know which can merge general relativity and quantum mechanics!
Something about the balance of strength:
回覆刪除The larger the impact, the larger the amplification of the reaction.
The weaker the impact, the less the amplification of the reaction.
The distance between impact of two opponents is somehow like the braking
distance of a speeding car.
[版主回覆06/09/2010 23:46:00]In the quantum world, the "normal" relation in the macro-wrold seems completely reversed. The shorter/smaller the distance between two interacting "particles" (just one way of describing the relevant force/energy), the greater the energy. Although there is a kind of symmetry in terms of force, a lot of very strange things happen: they often have to work through what I'd call "catalyst" particles which "lend" their energies for extremely brief moments of time for certain interactions between certain other extremely transient "particles" and after which they "get back" their energy and remain exactly the same as before the relevant reaction/interactions. And the extremely tiny energies get folded many times into the curved "spaces" of other particles (curved because their energies are so very big that they "bend" the relevant spaces of the other particles). It's really fascinating to read about them. Stranger than even the strangest fiction!