Vesselin Petkov, 06.01.2016

*Minkowski Institute, Montreal, Canada*

*I cannot avoid the suspicion that the mathematical elegance is obtained by a short cut which does not lead along the direct route of real physical progress. From a recent conversation with Einstein I learn that he is of much the same opinion.*

A.S. Eddington*, The Mathematical Theory of Relativity* 2nd ed. (Cambridge University Press, Cambridge 1924), p. 257 (new publication – 2016).

String theory constitutes an unprecedented case in the history of physics – while string theorists all admit that their theory has not been experimentally confirmed they behave as if this has already been done (or will certainly be done) and string theory has been treated on equal footing with the established physical theories. In recent years there has been a growing dissatisfaction among physicists with the attempts to regard hypothetical theories (such as string theory and the multiverse cosmology), which have not been experimentally confirmed, as if they were already accepted physical theories.*

String theory’s inability to make experimentally feasible predictions was nicely summarized by the Nobel prize winner Sheldon Glashow: “Sadly, I cannot imagine a single experimental result that would falsify string theory. I have been brought up to believe that systems of belief that cannot be falsified are not in the realm of science.”

In fact, not only *predictions* of string theory can be used to test it. Everyone agrees that a necessary condition that should be met by any proposed physical theory is that it should not contradict the *existing* theoretical and experimental evidence. It is precisely here where I think opportunities to test whether string theory contradicts the existing experimental facts might have been missed.

Let me give just one example. While string theorists have extensively studied how the interactions in the hydrogen atom can be represented in terms of the string formalism, I wonder how string theorists would answer a much simpler question – what should the electron (according to string theory) be in the ground state of the hydrogen atom? I think answering this question will reveal that **string theory contradicts the experimental fact that the hydrogen atom does not possess an electric dipole moment in its ground state** – if the electron were a miniature string** (according to string theory) it would be **localized** somewhere above the proton and the charges of the electron and the proton would inescapably form an electric dipole (in contradiction with experiment).

As string theory regards the electron as **localized** in an area much smaller than 10^(-18) m (due to its being a string of such dimensions), **string theory already contradicts all experimental evidence proving that the electron **(for example)** is not a localized entity** (as in the ground state of the hydrogen atom).

We all know that the final decision in Physics is made by the **Ultimate Judge – the experimental evidence:**

*If a proposed theory (regardless of its perceived beauty and elegance, supposed explanatory power, number of supporters and number of MSc and PhD theses on this theory) contradicts even a single experimental fact, it is over.*

More on the debate:

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* In December 2014 George Ellis and Joe Silk published in *Nature* the article Scientific method: Defend the integrity of physics, whose beginning openly expressed that dissatisfaction and alarm: “This year, debates in physics circles took a worrying turn. Faced with difficulties in applying fundamental theories to the observed Universe, some researchers called for a change in how theoretical physics is done. They began to argue – explicitly – that if a theory is sufficiently elegant and explanatory, it need not be tested experimentally, breaking with centuries of philosophical tradition of defining scientific knowledge as empirical.”

** Unlike quantum mechanics, string theory makes a clear claim about what an electron, for example, is – a miniature string. Because of this explicit claim string theory contradicts the experimental evidence. Quantum mechanics avoids such a contradiction, because it deals with the *states* of the electron, not directly with the electron itself (there is no spacetime model of the electron in quantum mechanics, that is, quantum mechanics tells us nothing about what quantum objects *themselves* are). In the framework of quantum mechanics one may say that, in the above example, the hydrogen atom in s-state is a superposition of an infinite number of states (of the electron being at different locations above the proton). *But a superposition is a mathematical notion and, naturally, one is interested in the physics represented by this notion.* I see only two logically possible physical models of the electron that are consistent with the mathematical notion of superposition:

- The electron is a point-like object, which orbits the proton so rapidly that, for the time of measuring the electric dipole moment of the hydrogen atom, the electron completes a huge number of revolutions and the average dipole moment is zero. However, Erwin Madelung calculated the orbital velocity of the electron necessary to produce such an average effect and found that the electron should move at a velocity that is
*orders of magnitudes greater than the speed of light*.

*The electron does not exist*In other words, the electron should not be regarded as a worldline in spacetime, but as an ensemble of the points of its “disintegrated” worldline. These points are scattered all over the spacetime region where the electron wave function is different from zero. In the case of the hydrogen atom in s-state, the constituents of the electron’s “disintegrated” worldline form a “worldube”, consisting of those constituents, around the “worldtube” of the proton, consisting of the proton’s constituents; in the ordinary three-dimensional language, the electron’s constituents form a spherical shell around the proton, which means that there is no dipole moment in the s-state. As the**continuously**in time., we have another magical expression (in Minkowski’s words) –**probabilistic**distribution of the electron’s constituents is forever given in spacetime*predetermined probability*.