Once Before Time - Martin Bojowald [43]
But the extra dimensions imply a serious problem. Even though the mathematical equations of string theory for high-dimensional space-times are complicated, one can estimate how rich the set of all its solutions might be. One can count those solutions whose properties agree roughly with what we see in our universe. Unfortunately, the result is an unimaginably large number: There are more solutions than there are protons in the whole universe. Such a large variety renders the theory, as beautiful and unique as it may appear from a mathematical viewpoint, useless for physical explanations. There is simply no basis for concrete predictions, since unknown phenomena would in no way be restricted. Such a theory would literally be a theory of everything, for everything—anything—could happen in it.
Even if a theory is unique and does not give rise to different tone colors as the vibrating strings of musical instruments do, this advantage can easily be obliterated by the vast deluge of solutions. There may be just one solo instrument, but its keyboard is enormous. Numerous pieces can be played on it, and nobody knows which composition corresponds to our world or just how this could be determined. Maybe there appear to be so many solutions only because all the conditions mathematically required for string theory have not yet been established with the available methods. Researchers split into two camps at this point: those who unquestioningly believe in the uniqueness of string theory and its solutions, and who continue looking for the missing consistency conditions; and others who, following the example of Leonard Susskind, make a virtue of necessity. If no unique solution is to be identified with our observed universe, they argue, at least the “most likely” solution should agree with our world. Of course, this brings in a new difficulty: first defining the degree of likelihood mathematically, and then, if this can be done reliably, showing how one would recognize the likelihood from the observation of only one of all possible worlds. We devote the last chapters to the uniqueness question of theories and solutions. For now, we turn to an alternative theory addressing the quantum theoretical nature of the space-time stage head-on.
LOOP QUANTUM GRAVITY: ATOMS OF SPACE AND DARKNESS
And weave the life-garment of deity.
—GOETHE, Faust
Matter is made up of atoms. If no atoms are present in an empty region of space-time, a vacuum state is realized. In modern physics, the vacuum plays an important role as the base on which all matter configurations rest. Starting with a vacuum region and moving matter into it atom by atom, all possible complex constructs can be built up. (This can be understood as a thought process, but with modern nanotechnology it is actually possible in a literal sense by manipulating single atoms.)
A material atom has energy that it contributes to the piece of matter it helps to build up. The energy can increase in two different ways: We can enlarge the number of atoms by adding more of them, and with them their energy; or an existing atom can be excited to a more energetic state. Practically, the second way of increasing the energy is normally done by heating the material or shining light on it. Since the total energy is conserved, atoms must be moved from one region to another but cannot be created from nothing, and the light or heat must come from an external source. All this is a direct consequence of the quantum theory of matter, whose language is quantum field theory. While quantum mechanics describes individual particles and their