The Problems of String Theory

One of the greatest problems faced by string theorists is how to measure the tension of a string.

We know that if a string is stiffer, it has more potential energy. Thus the modern piano has a much more powerful sound than the harpishord because its strings are mounted upon a steel frame and are tightened with screws at the end of the steel frame to increase the string's tension so that when hit, it emits sounds which vibrate with much more force and much longer, amplified by the sound board of good quality wood to increase its resonance.  But the strings are so tiny that  there is no way we can pluck or hit its string to measure the amount of energy emitted. Therefore the only thing we can do is to do the reverse and work out its strength or tension indirectly from something known ie. from the force of gravity. And since the force of gravity found by empirical observation and measurement is very very weak , this implies that the strings must have an extremely high tension. Sherk and Schwarz thus work out that each string has a tension of a thousand billion billion billion billion (10³⁹⁾  tons or the Planck tension. Therefore fundamental strings are extremely stiff compared to those we normally encounter. This has at least three consequences. First,  the tension is so great that the string is curled in upon itself to a miniscule size of Planck length of 10³³ cm.

 

Second, quantum mechanics dictate that the energy of the string can only increase by definite discrete amounts or a multiple of the smallest energy unit. The force or energy of a string is  proportional to the tension of the string and also to the number of peaks and troughs in the particular vibrational pattern while the whole number multiple is determined by the amplitude of the vibrational pattern. The "smallest energy unit" happen to be Planck energy or 10¹⁹ times the mass of a proton. By quantum standards, this is a huge mass. It's normally called  the Planck mass or about equal to the mass of a grain of dust or a collection a colony of a million bacteria. If so, then how do we explain the abundance of such much lighter particles like electrons, quarks, photons etc in the universe?  

 

What the string theorists find is that owing to constant quantum jitters, there can be energy "cancellations" between such quantum jitters. More than that, they find that the energy associated with quantum jitters of a string is negative! Such cancellations reduce the overall energy of a vibrating string by roughly the Planck energy. So, the lowest net energy vibrations correspond to those found in the more familiar matter and force particle families mentioned above. Scherk and Schwarz found in the 1970s that for the vibrational pattern whose properties make it suitable as a candidate for the graviton messenger particle, the energy cancellations must be perfect so that there will be a zero mass gravitional force particle! It is only because the graviton is practically massless that it can travel at the speed of light. However in this world, low energy vibrational combinations are the exception rather than the rule: the more typical vibrating strings correspond to a particle whose mass is billion upon billions of times greater than that of the proton.What this means is that the lighter particles should arise in the mist above the roaring ocean of energetic strings. Thus even such a heavy particle like the top quark with a mass of about 189 times that of a proton, can only arise from a vibrating string if the Planck-scale energy is cancelled by quantum jitters by more than one part in a hundred million billion!

 

The third important consequence of the huge value of string tension is that strings can literally execute an infinite number of vibration patterns. If so, why is it that we do not have an infinite number of elementary particles? The answser lies with our existing technology. It does not allow us to discover an infinite number of particles because we are simply unable to reproduce the tremendous energies required for testing the existence of all the particles predicted by string theory. But we can posit that at the creation of the universe, situations existed wherein the energy levels were high enough to produce these particles. The only problem is that such particles would not have survived until now because super-heavy particles are usually unstable. They would usually decay into a number of smaller and ever lighter particles. The end result can be seen today in the form of those familiar particle we meet day in day out. But theoretically, such super-heavy particles could have existed.

 

However, the string theory also has its own limitation. Since the size pf a string is supposed to be about Planck's length, and its mass is about that of Planck mass and its force is about that of Planck force, this means that we cannot use the string to probe anything smaller than matter of shorter than sub-Planck-scale distance. We can only use a fine tipped instrument to probe the surface of rougher objects. We cannot use a blunt instrument to probe a finer object. If so, since the Planck scale is the smallest we can find by existing technology, that is the absolute limit of the kind of "particles" ( or strings) that our scientists can empirically find. If so, it cannot be affected by the supposedly disastrous short-distance quantum jitters in the same manner that our hand will find marble smooth although under a microscope, the marble surface will be found to be very grainy and full of pores. In the same manner, the sensitivity of strings to probe matter is limited by its Planck length: it cannot be used to probe distances shorter than Planck length. There is thus no way to explore the sub-Planck scale "imperfections" in the fabric of space. That however, does not necessarily mean that even smaller particles cannot exist. But it does means that even if they really do exist, we have no way of finding out about them by observation. All that we can do is to posit their possible existence through the use of mathematical logic! At present, that limit exists immediately above the level of the devastating "foam of the quantum sea", where all our known laws of physics applicable to the macroworld break down. The fluctuation of that sub-Planck size quantum sea can no longer be measured and for all practical purposes, do not "arise" from an empirical point of view.

 

According to Greene, we have this problem of the uncertainty of this violent sub-Planck quantum fluctuation partly because of the way we have been doing our physics. We previously see the world of matter and force in terms of point or billiard ball-like matter and force particles. Once we reach a scale no bigger than a point, with literally no spatial extent, our laws break down. On the tinest of scale, we run into insurmountable difficulties. But string theory tells us that we run into difficulties only because we do not really understand the true nature of matter and force. The new rules of quantum mechanics tell us that there is a limit to how finely we can probe the universe. We have been "misled" by our previous point-particle approach to grossly overstep the bounds of physical reality, by thinking of reality as continuous, by thinking analogically. Previously physicists like Pauli, Heisenberg, Dirac and Feynman found that it is very difficult to construct a theory of physical reality without positing a point particle in the macro-world which is consistent with the principles of conservation of quantum-mechanical probability( physical objects do not suddenly vanish from the universe: they merely change their form or mode of existence) and the impossibility of faster than light speed transmission of information. But they also found that once they reach the smallest limit of point particles, the results show that such laws appear to be violated e.g with what looks like faster than speed of light "communication" between particles etc. But now string theory has shown that these rules need not be broken and in addition, their theory can accomodate even the force of gravity!  

 

How does string theory do that? They envision the matter and energy as strings such that when in the former scenario of an electron and its anti-particle, the positron colliding, annihilating each other in a flash of energy, then emitting a photon which travels a bit more in space before releasing the energy it derived from the initial electron-positron pair by producing another electron-positron pair which travel on further deflected trajectories, the electron and positron are viewed as different oscillating loops, vibrating in just the right kind of resonance patterns and when they "collide", what they do is that they "merge" together to produce a third vibrating string (the photon string) and the photon string then dissociate into two further strings which travel on along like in the previous point-particle model, deflected trajectories . But whereas in the particle scenario, the point-particle is seen as occurring at a specific point in space and time, in the string scenario, when the strings interact, they do so at different times and different places (if seen from the point of view of the particle perspective). From the string theory point of view, when the two strings "merge", they do so at different places and times, more or less like waves cutting into each other at different angles at different points in time in different phases.  In short, according to Greene's explanations, "there is no unambiguous location in space and time or moment in time when the strings first interact" . It really depends on the state of motion of the "observer:" . Thus in a sense, string theory "smears" out the place(s) or location(s) where the relevant interactions are supposed to be taking place and is thus able to avoid the disastrous results of the "infinity" solutions often encountered when scientists adopt the kind of mathematical formulas employed to describe the behavior of such "point-particles" in accounting for the relevant quantum interaction of such "point-particles". Thus in a way, the force or punch of the "collision" is spread out along the length of the strings instead of being concentrated on one specific point in time and space and in the case of gravity, this smearing significantly dilutes the other quantum forces to such an extent that calculations will yield "well-behaved" finite answers instead of the previous "infinities."  This "smearing" smooths out the ultra-microscopic jitteriness of space as sub-Planck length distances are blurred together, according to Greene. The impossible and insoluble calculations which results in applying the relevant equations from the point-particle way of describing quantum particle interactions are thus "avoided" and even gravity can be accomodated within the string theory!