Lars-Göran Johansson, Uppsala University

2006-2011

Aim

The aim of this project has been to probe some philosophical issues relating to string theory. In particular, the following four questions has been in focus for this project:
1. So far, string theory has not produced any testable empirical consequences: could it nevertheless be justified as a scientific theory, or should we dismiss it, arguing that producing testable consequences is a sine qua non for a scientific theory?
2. String theory requires six extra spatial dimensions, which are compactified and thus not directly observable by present technology. What is the ontological status of these extra dimensions; are they just mathematical tools or do they have ontological significance?
3. String theory develops rapidly and something else than testing (which has not been possible) is the driving force. What is that? Lakatos philosophy will be used as a theoretical starting point.
4. String theory presently comes in five versions. These are related to each other in the form of dualities; the different versions seem to say quite different things, but they still predict the same particle spectra, symmetries and scattering amplitudes . What is the significance of these dualities? Are these five versions merely different formulations of one single theory, or do these version say different things, in which case we have underdetermination? If the former alternive is the correct one, how should we interpret statements that differ between different versions?

Important results

1. We have evaluated present string theory using the perspective of respectively logical positivism, falsificationism, Kuhn's theory about scientific revolutions and Lakatos methodology of scientific research programmes. Neither perspective can be used for dismissing string theory as unscientific or ripe for dismissal, despite is lack of empirically testable consequences. Conversely, string theory, being an ongoing research program where we do not know the final outcome, underlines the point that none of these four methodologies can be used as guidance in theory choice.
2. We have found rather strong reasons to hold that the extra compactified dimensions in string theory are merely mathematical auxiliaries with no counterparts in physical reality. One such reason is the AdS/CFT correspondence, which says that a theory formulated in a background of X dimensions is empirically equivalent to a conformal field theory in X-1 dimensions. These dimensions looks like a kind of 'gauge', serving a role analogous to for example the phase of the electromagnetic potential.
3. Different versions of string theory appear to say quite different things about for example string lengths or size of compactified dimensions. But since two dual versions predicts the same particles, symmetries, scattering amplitudes and other measureable quantities, we have found there is substantial reason to hold that dual versions of string theory are merely different formulations of one and the same theory, not different theories and hence not cases of underdetermination. However, no general criterion for theory equivalence is discussed.

The two most important papers are:

1. String Theory and General Methodology: a Mutual Evaluation
2. String Theory and Spacetime
The first paper is, as the title says, a mutual evaluation. On the one hand, four well-known general methodologies mentioned above under 'results' are used for assessing whether the lack of empirically testable consequences is reason enough to reject string theory or not. Somewhat surprisingly, the conclusion is that none of these methodologies recommend such a move. We have also looked at the situation from a converse perspective, using string theory an example of an ongoing research program about which we do not know the outcome, for assessing these four methodologies. This is profitable, because almost all arguments for or against a particular methodology, which uses concrete examples, use historically well-known episodes where we know the final outcome of the research program. When using string theory we don't know whether it will succeed or fail. Our verdict is that no general methodology so far proposed can be used for deciding whether to continue a research program or give up. This is perhaps unexpected, but since we don't think there can be any general solution to the induction problem, it is just as it should be.

String Theory and Spacetime
This paper consists of an analysis of the use of the concept of dimension in mathematics and in physics. It is uncontroversial that mathematical and physical dimensions are different things and the core issue in this context is what is required for a dimension in a mathematical theory to be interpreted as a theoretical representation of a dimension of physical space. String theory 'lives' on a background manifold having 10 dimensions. There are different versions having different topologies and different metrics on these dimensions; hence, if these versions of string theory merely are different theory formulations describing the same physics, then these topological and metrical properties of the extra dimensions cannot have physical significance. Our result is thus that there is little reason to hold that the compactified dimensions have any physical significance.

In addition to these two papers we have finalised one more paper. These three can be accessed at http://www.anst.uu.se/lajoh623/projekt

New research questions

During our research we have found two more aspects of string theory having philosophical relevance. The first is the landscape-hypothesis by Susskind and others. Since it is not possible to derive the values of the constants of nature from first principles, Susskind suggests that all possible combinations of these constants in fact are realised, and our world is just one among a huge number of existing such combinations. This speculative hypothesis has some similarities with the many-worlds interpretation of quantum mechanics. Also it shows some similarities with David Lewis modal realism. One of us, Matsubara has started to work on paper discussing these things.

The other aspect is the strong desire among string theorists, and physicists in general, to unite all of physics into one single theory. Only if this goal is reached we have a satisfactory explanation of everything physical, they seem to think. Thus it appears that one particular model for scientific explanation, unification, first suggested by Friedman and Kitcher, may fit quite well actual views among physicists. There are well-known difficulties in formulating a satisfactory theory for explanation as unification, but reflection on string theory has given us inspiration and some new ideas on this topic. A paper with the tentative title 'Explanation, unification and string theory' is under way.

Publications

Lars-Göran Johansson and Keizo Matsubara:
1. ‘String theory and general methodology: a mutual evaluation.’, in Studies in History and Philosophy of Modern Physics 42 (2011) 199–210.
2. ‘String theory and spacetime.’ Submitted to Philosophy of Science
3. K. Matsubara: ‘Realism, underdetermination and string theory dualities.’ Submitted to Synthese.
These papers can be found at http://www.anst.uu.se/lajoh623/projekt/

Work still in progress:
K. Matsubara: ’The many worlds of Physics and Philosophy.’
L-G Johansson: ‘Explanation, Unification and String Theory.’