M-theory/string theory a work in progress
It should be remembered that, despite all its refinement over the last 30 years, string theory remains a theory in progress, not yet tested by experimental confirmation. “It has yet to make definitive predictions whose experimental investigation could prove the theory right or wrong and we are still at an early stage in our attempt to meld quantum physics and gravity. For all its advances, it remains a wholly mathematical theory and will remain speculative until a convincing link to experiment or observation is forged”[1].
There is nothing novel about this in the scientific world. Indeed, Einstein invented the theory of general relativity by sitting at his desk, thinking out the problem and then working out the mathematics from first principles. Its first real experimental test did not come for years[2]. Science has a long history of predicting things like the existence of particles and happenings in the cosmos which in the fullness of time have later proved to be correct following experiment, testing and observation.
So far as the theory’s inability to produce falsifiable predictions after 30 years is concerned, my view is that we need to be more patient. Given the miniscularity of the putative entities involved (quivering strings), I don't think this should come as much of a surprise. It is, after all, a classic work-in-progress and I think we should recognise that and be patient with it. The very existence of the atom itself was unconfirmed not much more than a hundred years ago, let alone the 17 elementary particles (including the recently discovered new particle, supposing it to be the Higgs) we now have.
[1] Greene (2011), 72, 101, 249.
[2] Michael Moyer, “Is space digital?” Scientific American, Feb 2012, 20 at 26.
Science and mathematical predictions in general
In fact the scientific world is replete with instances where purely mathematical calculations later - much later - provided just the right tools the physicists needed. In the Elegant Universe, Brian Greene describes an instance where in 1968 a young theoretical physicist by the name of Gabriele Veneziano was trying to make sense of some aspects of the strong nuclear force. He came a cross a long forgotten formula devised for purely mathematical purposes by the Swiss mathematician Leonhard Euler some 200 years before (the Euler beta-function), and much to his surprise found that it seemed to describe numerous properties of the strongly interacting particles in one go.
Without having any realisation of its practical manifestations, Euler’s observation encapsulated mathematically many features of the strong nuclear force. This was in fact the genesis of string theory, and in 1970, a number of researchers revealed the hitherto unknown physics behind Euler's formula. They showed that if one modelled elementary particles as little, vibrating one-dimensional strings, their nuclear interactions could be described exactly by Euler's function. If the pieces of string were small enough, they reasoned, they would still look like point particles.
In the May 2011 edition of the Scientific American, there is an article describing a numbers system called octonians devised by a young mathematician and physicist William Rowan Hamilton in 1843 which is now thought to provide an explanation as to why our universe could have 10 dimensions[1]. For more than a century octonians provided no more than intellectual exercise to mathematicians, and (so says the article) it took the development of modern particle physics, in particular string theory, to see how octonians might be useful in the real world, thereby providing a theoretical basis coinciding with M-theory which postulates 11 dimensions.
There is nothing novel about this in the scientific world. Indeed, Einstein invented the theory of general relativity by sitting at his desk, thinking out the problem and then working out the mathematics from first principles. Its first real experimental test did not come for years[2]. Science has a long history of predicting things like the existence of particles and happenings in the cosmos which in the fullness of time have later proved to be correct following experiment, testing and observation.
So far as the theory’s inability to produce falsifiable predictions after 30 years is concerned, my view is that we need to be more patient. Given the miniscularity of the putative entities involved (quivering strings), I don't think this should come as much of a surprise. It is, after all, a classic work-in-progress and I think we should recognise that and be patient with it. The very existence of the atom itself was unconfirmed not much more than a hundred years ago, let alone the 17 elementary particles (including the recently discovered new particle, supposing it to be the Higgs) we now have.
[1] Greene (2011), 72, 101, 249.
[2] Michael Moyer, “Is space digital?” Scientific American, Feb 2012, 20 at 26.
Science and mathematical predictions in general
In fact the scientific world is replete with instances where purely mathematical calculations later - much later - provided just the right tools the physicists needed. In the Elegant Universe, Brian Greene describes an instance where in 1968 a young theoretical physicist by the name of Gabriele Veneziano was trying to make sense of some aspects of the strong nuclear force. He came a cross a long forgotten formula devised for purely mathematical purposes by the Swiss mathematician Leonhard Euler some 200 years before (the Euler beta-function), and much to his surprise found that it seemed to describe numerous properties of the strongly interacting particles in one go.
Without having any realisation of its practical manifestations, Euler’s observation encapsulated mathematically many features of the strong nuclear force. This was in fact the genesis of string theory, and in 1970, a number of researchers revealed the hitherto unknown physics behind Euler's formula. They showed that if one modelled elementary particles as little, vibrating one-dimensional strings, their nuclear interactions could be described exactly by Euler's function. If the pieces of string were small enough, they reasoned, they would still look like point particles.
In the May 2011 edition of the Scientific American, there is an article describing a numbers system called octonians devised by a young mathematician and physicist William Rowan Hamilton in 1843 which is now thought to provide an explanation as to why our universe could have 10 dimensions[1]. For more than a century octonians provided no more than intellectual exercise to mathematicians, and (so says the article) it took the development of modern particle physics, in particular string theory, to see how octonians might be useful in the real world, thereby providing a theoretical basis coinciding with M-theory which postulates 11 dimensions.
Plaque commemorating William Rowan Hamilton's discovery of the fundamental formula underlying quaternion multiplication underpinning octonians. The idea came to him in a flash ah he was walking along the canal here at Broombridge, Dublin, Ireland on 18 October 1843, so he scratched them onto the stonework of the bridge. Photographed by the author, 30 May 2013.
Another aspect of the reasoning behind this is the idea of supersymmetry: that the universe exhibits a symmetry between matter and the forces of nature, and that the laws of physics would remain essentially unchanged if we exchanged all the matter and force particles for one another, rather like viewing the universe in a strange mirror[2].
Another example which has already been visited: in 1931 Paul Dirac mathematically predicted the positron, which arose from his work in solving the mathematical equations relevant to the motions of electrons. The maths threw up an extraneous solution describing the motion of a particle just like the electron but with a positive charge. The following year that very particle was discovered through experiment by Carl Anderson, but Dirac’s mathematics foreshadowed its existence[3].
And finally, the best example of all: Einstein's field equations for general relativity actually predicted on their own the fact that the universe was expanding, but he wouldn't accept them. Fortunately or unfortunately for him, he only had to wait a couple of decades for them to be proved wrong by Hubble's observations. The shame is that in dealing with the microworld, we don't have the luxury of a large enough microscope to falsify string theory's mathematical predictions.
[1] John C. Baez and John Harris, “The strangest numbers in String Theory”, Scientific American, May 2011, 46-49.
[2] See preceding discussion of supersymmetry.
[3] See the account given by Dana Mackenzie, The Universe in Zero Words – The story of Mathematics, Elwin Street Productions, Sydney, 2012, 164ff. .
Another example which has already been visited: in 1931 Paul Dirac mathematically predicted the positron, which arose from his work in solving the mathematical equations relevant to the motions of electrons. The maths threw up an extraneous solution describing the motion of a particle just like the electron but with a positive charge. The following year that very particle was discovered through experiment by Carl Anderson, but Dirac’s mathematics foreshadowed its existence[3].
And finally, the best example of all: Einstein's field equations for general relativity actually predicted on their own the fact that the universe was expanding, but he wouldn't accept them. Fortunately or unfortunately for him, he only had to wait a couple of decades for them to be proved wrong by Hubble's observations. The shame is that in dealing with the microworld, we don't have the luxury of a large enough microscope to falsify string theory's mathematical predictions.
[1] John C. Baez and John Harris, “The strangest numbers in String Theory”, Scientific American, May 2011, 46-49.
[2] See preceding discussion of supersymmetry.
[3] See the account given by Dana Mackenzie, The Universe in Zero Words – The story of Mathematics, Elwin Street Productions, Sydney, 2012, 164ff. .