String theory contradicts experiment

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:


 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 continuously in time. 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 probabilistic distribution of the electron’s constituents is forever given in spacetime, we have another magical expression (in Minkowski’s words) – predetermined probability.

Is gravity a physical interaction?

Vesselin Petkov, 28.12.2015

Minkowski Institute, Montreal, Canada

Although it may look heretical to some, one of the ways to deal with the unsuccessful attempts to create a theory of quantum gravity is to question and examine rigorously the taken-for-granted  assumption that gravity is a physical interaction [1].

If Einstein had examined thoroughly Minkowski’s profound idea of regarding four-dimensional physics as spacetime geometry he would have most probably considered and carefully analyzed the possibility that gravitational phenomena may not be caused by gravitational interaction since they are nothing more than mere manifestations of the curvature of spacetime. Had he lived longer, Minkowski himself would have almost certainly arrived at this radical possibility by reformulating Einstein’s general relativity in a similar way as he reformulated Einstein’s special relativity. In 1921 Eddington even stated almost explicitly that gravity is not a physical interaction – “gravitation as a separate agency becomes unnecessary” [2].

Here is a summary of the argument (for more details see [3]; see also “Do gravitational waves carry gravitational energy and momentum?):

Gravitational phenomena are fully explained in general relativity as mere effects of the non-Euclidean geometry of spacetime and no additional hypothesis of gravitational interaction is necessary :

  • according to the geodesic hypothesis [4] in general relativity, a particle, whose timelike worldline is geodesic, is a free particle moving by inertia; therefore the motion of bodies falling toward the Earth’s surface and of planets orbiting the Sun (whose worldlines are geodesic) is inertial, i.e., interaction-free, because the very essence of inertial motion is motion which does not involve any interaction whatsoever;
  • if changing the shape of a free body’s geodesic worldtube (from straight timelike geodesic to curved timelike geodesic) by the spacetime curvature induced, say, by the Earth’s mass (which causes the body’s fall toward the Earth’s surface) constituted gravitational interaction, that would imply some exchange of gravitational energy and momentum between the Earth and the body, but such an exchange does not seem to occur because the Earth’s mass curves spacetime irrespective of whether or not there are other bodies in the Earth’s vicinity (which means that, if other bodies are present in the Earth’s vicinity, no additional energy-momentum is required to change the shape of the geodesic worldtubes of these bodies and therefore no gravitational energy-momentum is transferred to / exchanged with those bodies; see [3]). In other words, the Earth’s mass changes the geometry of spacetime around the Earth’s worldtube and it does not matter whether the geodesics (which are no longer straight in the new spacetime geometry) around the Earth are “empty” or “occupied” by particles of different mass, that is, in general relativity “a geodesic is particle independent” [6].


1. It is not inconceivable that gravity may turn out not to be a physical interaction. This heretical option should legitimately be on the research table in these difficult times in fundamental physics – decades with no major breakthroughs in fundamental physics as revolutionary as the theory of relativity and quantum mechanics (despite the efforts of many brilliant physicists). The failures so far to create a theory of quantum gravity may have a simple but unexpected explanation – gravitation is not a physical interaction and therefore there is nothing to quantize.

2. A. S. Eddington, “The Relativity of Time,” Nature 106, 802-804 (17 February 1921); reprinted in: A. S. Eddington, The Theory of Relativity and its Influence on Scientific Thought: Selected Works on the Implications of Relativity (Minkowski Institute Press, Montreal 2015). Two years later, in his fundamental work on the mathematical foundations of general relativity The Mathematical Theory of Relativity (Cambridge University Press, Cambridge 1923) [7] Eddington stated it even more explicitly (p. 221): “An electromagnetic field is a “thing;” gravitational field is not, Einstein’s theory having shown that it is nothing more than the manifestation of the metric.”

3. V. Petkov, “Physics as Spacetime Geometry,” in: A. Ashtekar, V. Petkov (eds), Springer Handbook of Spacetime (Springer, Heidelberg 2014), Chapter 8, pp. 141-163. See also “Is Gravitation Interaction or just Curved-Spacetime Geometry?

4. The geodesic hypothesis is regarded as “a natural generalization of Newton’s first law” [5], that is, “a mere extension of Galileo’s law of inertia to curved spacetime” [6]. The geodesic hypothesis has been confirmed by the experimental fact that particles falling toward the Earth’s surface offer no resistance to their fall – a falling accelerometer, for example, reads zero resistance (i.e. zero acceleration; the observed apparent acceleration of the accelerometer is caused by the spacetime curvature caused by the Earth). The experimental fact that particles do not resist their fall (i.e. their apparent acceleration) means that they move by inertia and therefore no gravitational force is causing their fall. It should be emphasized that a gravitational force would be required to accelerate particles downwards only if the particles resisted their acceleration, because only then a gravitational force would be needed to overcome that resistance.

5. J. L. Synge, Relativity: The General Theory (Nord-Holand, Amsterdam 1960) p. 110.

6. W. Rindler, Relativity: Special, General, and Cosmological (Oxford University Press, Oxford 2001) p. 178.

7. New publication: Arthur S. Eddington, The Mathematical Theory of Relativity (Minkowski Institute Press, Montreal 2016).