*Minkowski Institute, Montreal, Canada*

If Minkowski had a chance to look (from the higher reality of his “die *Welt*,” i.e., spacetime) at the research strategy of the Institute named after him, I hope he would be delighted to see that along with his own way of doing physics (exploring the internal logic of the mathematical formalism of physical theories) and Einstein’s analyses of thought experiments, the strategy also fully exploits Wheeler’s “first moral principle” [1] – *“Never make a calculation until you know the answer.”*

I think this principle is enormously powerful when dealing with issues such as (for example):

- The status of rotation in spacetime physics (not in general relativity, where the old 3+1 way of thinking is still allowed to try to complicate things). The issue of rotation is clear in spacetime (no calculations needed): it is the planets that orbit the Sun because their worldtubes are helixes around the worldtube of the Sun.

- Conventionality of simultaneity – no calculations are needed to demonstrate that it is a matter of convention (as Einstein held) which events of spacetime are regarded as simultaneous (the fact that simultaneity is a matter of convention implies that the one-way velocity of light is also a matter of convention, which is self-evident in spacetime physics, where light is adequately represented by null geodesics; one-way velocity of light is a notion in the old 3+1 way of thinking). Any claim that simultaneity is relative but not conventional amounts to a contradiction in terms: there is no objectively privileged class of simultaneous events (due to relativity of simultaneity), but there is an objectively privileged class of simultaneous events (due to the non-conventionality of simultaneity).

**References**

1. E.F. Taylor, J.A. Wheeler, *Spacetime Physics*, 2nd ed. (W.H. Freeman & Company, New York 1992), p. 20

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*Minkowski Institute, Montreal, Canada*

One often hears the question of whether physics has shown that time does not exist.

The 1908 famous lecture “Space and Time” ( PDF) by Hermann Minkowski (Einstein’s mathematics professor) made it possible to answer this question:

- Time is very much real since it does exist as the fourth dimension of a
four-dimensional world whose existence was discovered by Minkowski who successfully decoded the hidden message of all failed experiments to discover absolute motion in the absolute space: those experiments failed because there is no such thing as an absolute (single) space in the world; all observers in relative motion have their own spaceS and timeS, which is possible in a real for-dimensional world. Here are Minkowski’s own words:“Hereafter we would then have in the world no more*real*space, but an infinite number of spaces analogously as there is an infinite number of planes in three-dimensional space. Three-dimensional geometry becomes a chapter in four-dimensional physics.”*the* - What does not exist is the
of time since there is no such thing in the four-dimensional world in which*flow*(forming the fourth dimension).*all moments of time have equal existence*

It should be stressed that it is the experimental evidence that forced Minkowski to conclude that the world is four-dimensional; now the experimental proof of the higher four-dimensional reality is truly irrefutable – the experiments that confirmed the relativistic effects would be ** impossible** if reality were a three-dimensional world (evolving in time) – see “The world is four-dimensional – Hermann Minkowski’s irrefutable proof” (Minkowski Institute – Foundational Knowledge – Minkowski’s Proof).

For those who wonder how we could perceive that time flows, if all events of spacetime exist equally, here is Hermann Weyl’s explanation (which does raise the question of the nature of consciousness, but nevertheless it is the only meaningful explanation):

“The objective world merely exists, it does not happen; as a whole it has no history. Only before the eye of the consciousness climbing up in the world line of my body, a section of this world “comes to life” and moves past it as a spatial image engaged in temporal transformation.”

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*Minkowski Institute, Montreal, Canada*

The issue of relativistic mass (recently being questioned by an increasing!? number of physicists) is one more example of the kind of questions that are being analyzed at the Minkowski Institute.

Here is my personal position on the issue with which I enter the discussions at the Minkowski Institute. Once the position of the Minkowski Institute has been determined (after a rigorous examination of the existing theoretical and experimental evidence), it will be announced.

The fact [1] of the relativistic increase of mass is one of the deepest open questions in spacetime physics. Research on it is physics at its best.

Trying to deny the fact that mass increases with velocity or to declare it a matter of taste or fashion is, I think, physics at its worst, because a potentially groundbreaking research direction is excluded from the very beginning.

It is true that physics at its best also includes the ability to identify and rule out research directions based on misconceptions, but for reasons summarized below (and explained in detail in a book near completion: Introduction to Spacetime Physics) I do not think the relativistic increase of mass is a misconception.

On the contrary, the recent fashion to claim that mass does not increase with velocity is, I think, an unfortunate and embarrassing misconception.

When two facts are taken explicitly into account:

- the very definition of mass (that
)*mass is defined as the measure of the resistance a particle offers to its acceleration* - that in relativity acceleration is different in different reference frames

it becomes immediately clear that the mass of a particle cannot be the same in all frames in relative motion.

Proper or rest mass (which is an invariant) and relativistic mass (which is frame-dependent) are exactly like proper time (which is an invariant) and relativistic / coordinate time (which is frame-dependent) [and, to some extent, like proper and relativistic length].

**References**

[1] The fact is that an increasing force should be applied to a particle to accelerate it to speeds close to the speed of light. As Newton first realized it, to accelerate a particle, a force is needed to * overcome* the particle’s

.

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Minkowski Institute, 21.03.2016

In an interesting recent publication (Mahler et al., *Science Advances*, 19 Feb 2016, Vol. 2, no. 2) Aephraim Steinberg (University of Toronto) and collaborators perform a remarkable double-slit experiment on entangled photons, measuring trajectories that some have termed “surreal”. They claim that “the trajectories seem surreal only if one ignores their manifest nonlocality”.

However one should be careful about what type of nonlocality one speaks of. I do not see where the experiment points to non-locality in the strong sense of superluminal interactions. I believe the measured effects of entanglement can be explained by long-range correlations – which also exist in countless classical systems. For instance, in recently discovered fluid-mechanical systems involving oil droplets bouncing on a vibrating oil film (and mimicking a wide range of quantum phenomena), these correlations exist (cf. http://link.springer.com/article/10.1007%2Fs10701-015-9973-7). Such correlations are long-range or ‘delocalized’ but not non-local in the strong sense.

The Steinberg experiments do however give credit to de Broglie – Bohm theory, since this is the most natural theory to calculate trajectories (which in principle do not exist according to Copenhagen). It is usually believed Bohm’s theory is nonlocal because if one changes a boundary condition somewhere in the universe, the quantum potential (based on the wave function) ‘instantaneously changes’. But in exactly the same mathematical way, if you change the boundary conditions of a fluid somewhere, the ‘fluid field solutions instantaneously differ’. de Broglie – Bohm theory is not more non-local than fluid mechanics (cf. some ideas here: http://philpapers.org/archive/VERMOD.pdf). A common denominator between de Broglie’s theory and the droplet experiments is the existence of some kind of background field (quantum vacuum, ether or surface wave). Such a background presenting long-range correlations can indeed explain the Bell experiment in a local manner, it seems: cf. http://link.springer.com/article/10.1007%2Fs10701-015-9973-7.

In all the above you don’t need nonlocality in the strong sense. Therefore I prefer Bohm’s term ‘quantum wholeness’, which does not overtly violate relativity theory.

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*Minkowski Institute, Montreal, Canada*

This is another example of the kind of questions that are being analyzed at the Minkowski Institute – on the one hand, it is believed that black holes exist, especially after the recent detection of gravitational waves (initially almost unanimously regarded as a signature of black holes, but now it was shown that that might not be the case [1]); on the other hand, however, a careful (Minkowski-type) examination of the Schwarzschild solution of the Einstein equations in general relativity reveals that the two major problems with it cannot be easily brushed aside:

1. The Schwarzschild solution contains a singularity and perhaps most relativists feel very uneasy about this fact, because the existence of a singularity in a physical theory [2] is a clear sign that the theory breaks down in the circumstances where the singularity appears. The authors of a recent attempt [3] to free general relativity of singularities stated their motivation clearly: “We believe that *no acceptable physical theory should have a singularity (!)*, not even a coordinate singularity of the type discussed above! The appearance of a singularity shows the limitations of the theory.”

2. The Schwarzschild solution implies that there exist ** two realities** inside and outside the Schwarzschild sphere of radius

“We see that the Schwarzschild solution for empty space can be extended to the region *r < 2m*. But this region cannot communicate with the space for which *r > 2m*. Any signal, even a light signal, would take an infinite time to cross the boundary *r = 2m*, as we can easily check. Thus we cannot have direct observational knowledge of the region *r < 2m*. Such a region is called a black hole, because things may fall into it (taking an infinite time, by our clocks, to do so) but nothing can come out.

The question arises whether such a region can actually exist. All we can say definitely is that the Einstein equations allow it. A massive stellar object may collapse to a very small radius and the gravitational forces then become so strong that no known physical forces can hold them in check and prevent further collapse. It would seem that it would have to collapse into a black hole. It would take an infinite time to do so by our clocks, but only a finite time relatively to the collapsing matter itself.”

So, here is the second major problem with black holes explicitly formulated – *as we are (and always have been) distant observers it will take an infinite time for black holes to form, which, in ordinary language, means that black holes will never exist for us*.

In the second reality of the falling observers, according to general relativity, black holes will form.

I wonder whether there will be physicists and (perhaps more probably) philosophers who would claim that reality is *observer-dependent*. But even if this were the case, black holes would never exist in our reality, because this follows from general relativity – the same theory that predicts the very existence of black holes. More rigorously stated, the Schwarzschild solution of the Einstein equations in general relativity predicts ** both** (i) black holes, and (ii) that they will never form for distant observers.

What strikes me is that there are colleagues who freely talk about black holes perhaps without realizing that they are employing double standards with respect to the meaning of “take an infinite time”:

- From Dirac’s quote above: “Any signal, even a light signal, would take an infinite time to cross the boundary
*r = 2m*” – in this case “take an infinite time” is interpreted to mean ““; so*never**only*according to this interpretation even light will*never*escape from the Schwarzschild sphere, which allows one to talk about black holes.

- Again from Dirac’s quote above: “It would seem that it would have to collapse into a black hole. It would take an infinite time to do so by our clocks” – in this case “take an infinite time” inexplicably is
*not*taken to mean “” as above; instead, it is assumed without any justification that black holes exist.*never*

For more on whether or not black holes exist see [7-9].

**References **

[1] Vitor Cardoso, Edgardo Franzin, and Paolo Pani, “Is the Gravitational-Wave Ringdown a Probe of the Event Horizon?” Phys. Rev. Lett. **116**, 171101 (2016) and also Synopsis: Did Black Hole “Mimickers” Produce LIGO Signal?

[2] Robert Geroch, What is a Singularity in General Relativity? *Annals of Physics* **48** (1968) 526-540

[3] P.O. Hess, M. Schäfer, W. Greiner, *Pseudo-Complex General Relativity* (Springer, Heidelberg 2016). See the essence of the approach: W. Greiner, P.O. Hess, M. Schäfer,T. Schönenbach and G. Caspar, “There are No Black Holes – Pseudo-Complex General Relativity”, in: P. Nicolini, M. Kaminski, J. Mureika, M. Bleicher (eds), *1st Karl Schwarzschild Meeting on Gravitational Physics* (Springer, Heidelberg 2016) pp. 33-42

[4] In addition to this problem, Papapetrou also and particularly emphasizes the serious anomaly on the Schwarzschild sphere, whose physical meaning, I think, has not been thoroughly examined – “But these geodesics are space-like for *r > 2m* and time-like for *r < 2m. *The tangent vector of a geodesic undergoes parallel transport along the geodesic and consequently it cannot change from a time-like to a space-like vector. It follows that the two regions *r > 2m* and *r < 2m* do not join smoothly on the surface *r = 2m.*” [5]

[5] A. Papapetrou, *Lectures on General Relativity* (Reidel, Dordrecht 1974) pp. 85-86

[6] P.A.M. Dirac, *General theory of relativity* (Princeton University Press, Princeton 1996) pp. 35-36

[7] Stephen Hawking: ‘There are no black holes’

[8] Backreaction of Hawking Radiation on a Gravitationally Collapsing Star I: Black Holes? (Black holes cannot form)

[9] No Such Thing as a Black Hole? and Researcher shows that black holes do not exist

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*Minkowski Institute, Montreal, Canada*

*A Minkowski-type analysis of the mathematical formalism of general relativity implies that there is no gravitational energy and momentum, which in turn implies that gravitational waves cannot carry gravitational energy and momentum.*

The recent detection of gravitational waves reported earlier this week (12 February 2016) in the *Physical Review Letters* paper “Observation of Gravitational Waves from a Binary Black Hole Merger” should stimulate a closer scrutiny of the century-old open question – why the mathematical formalism of general relativity stubbornly refuses to yield a valid mathematical expression (representing a real feature of the world) for gravitational energy and momentum.

Had he lived longer Minkowski would have certainly loved to examine this question and might have arrived at a reformulation of Einstein’s general relativity in a way similar to his reformulation of Einstein’s special relativity.

This is precisely the type of open questions that are being thoroughly analyzed at the *Minkowski Institute* – on the one hand, it is taken for granted that gravitational energy and momentum self-evidently exist, but there is some annoying difficulty to represent them in a proper mathematical form; on the other hand, however, an analysis of the mathematical formalism of general relativity (following Minkowski’s example of analyzing the mathematical formalism of Newtonian mechanics that led him to revealing the true physical nature of Einstein’s special relativity as a theory of flat spacetime) demonstrates that there is no room for gravitational energy and momentum in general relativity:

- There is no proper tensorial expression (which represents a real physical quantity) for gravitational energy and momentum; for 100 years no one has managed to find such an expression.
- 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*(and therefore of gravitational energy and momentum) is necessary (as Eddington put in 1921 “gravitation as a separate agency becomes unnecessary” [1]):- according to the geodesic hypothesis [2] in general relativity, a particle, whose 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 geodesic to curved 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 [5]). 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” [4].

- according to the geodesic hypothesis [2] in general relativity, a particle, whose worldline is geodesic,is a
- The fact that “in relativity there is no such thing as the force of gravity” [3, p. 109] implies that there is no gravitational energy either since such energy is defined as the work done by gravitational forces.

Despite the above facts, the prevailing view among relativists is that there exists *indirect* astrophysical evidence for the existence of gravitational energy – coming from the interpretation of the decrease of the orbital period of the binary pulsar system PSR 1913+16 discovered by Hulse and Taylor in 1974 (and other such systems discovered after that), which is believed to be caused by the loss of energy due to gravitational waves emitted by the system (which carry away gravitational energy).

This interpretation that gravitational waves carry gravitational energy should be carefully scrutinized by taking into account the above arguments against the existence of gravitational energy and momentum and especially the fact that there does not exist a rigorous (analytic, proper general-relativistic) solution for the two body problem in general relativity. I think the present interpretation of the decrease of the orbital period of binary systems contradicts general relativity, particularly the geodesic hypothesis and the experimental evidence which confirmed it, because by the geodesic hypothesis the neutron stars, whose worldlines had been regarded as *exact* geodesics (since the stars had been modeled dynamically as a pair of orbiting *point* masses), *move by inertia without losing energy since the very essence of inertial motion is motion without any loss of energy*. For this reason no energy can be carried away by the gravitational waves emitted by the binary pulsar system. Let me stress it as strongly as possible: *the geodesic hypothesis and the assertion that bodies, whose worldlines are geodesic, emit gravitational energy (carried away by gravitational waves), cannot be both correct.*

In fact, it is the very assumption that *the binary system emits* *gravitational waves* which contradicts general relativity in the first place, because *motion by inertia does not generate gravitational waves* in general relativity. The inspiralling neutron stars in the binary system were modeled (by Hulse and Taylor) as *point* masses and therefore their worldlines are *exact* geodesics, which means that *the stars move by inertia* *and no emission of gravitational radiation is involved; *if the stars were modeled as *extended* bodies, then and only then they would be subject to tidal effects and energy would be involved, but that energy would be negligibly small (see next paragraph) and would not be gravitational (see the explanation of the origin and nature of energy in the sticky bead argument below). So, the assertion that the inspiralling neutron stars in the binary system PSR 1913+16 generate gravitational waves is incorrect because it contradicts general relativity. Gravitational waves are emitted * only* when the stars’ timelike worldlines are

Let me repeat it: when the stars follow their orbits in the binary system, they do not emit gravitational waves since they move by inertia according to general relativity (their worldlines are geodesic and no absolute acceleration is involved); even if the stars were modeled as extended bodies, the worldlines of the stars’ constituents would not be geodesic (but slightly deviated from the geodesic shape) which will cause tidal friction in the stars, but the gravitational waves generated by the very small absolute accelerations of the stars’ constituents will be negligibly weak compared to the gravitational waves believed to be emitted from the inspiraling stars of the binary system (that belief arises from* using not the correct general-relativistic notion of acceleration, but the Newtonian one*).

The famous sticky bead argument has been regarded as demonstrating that gravitational waves carry gravitational energy (because it is converted through friction into heat energy):

“The thought experiment was first described by Feynman (under the pseudonym “Mr. Smith”) in 1957, at a conference at Chapel Hill, North Carolina. His insight was that a passing gravitational wave should, in principle, cause a bead which is free to slide along a stick to move back and forth, when the stick is held transversely to the wave’s direction of propagation. The wave generates tidal forces about the midpoint of the stick. These produce alternating, longitudinal tensile and compressive stresses in the material of the stick; but the bead, being free to slide, moves along the stick in response to the tidal forces. If contact between the bead and stick is ‘sticky’, then heating of both parts will occur due to friction. This heating, said Feynman, showed that the wave did indeed impart energy to the bead and rod system, so it must indeed transport energy.” [8]

However, a careful examination of this argument reveals that kinetic, not gravitational, energy is converted into heat because a gravitational wave changes the shape of the geodesic worldline of the bead and the stick prevents the bead from following its *changed* geodesic worldline, i.e., *prevents the bead from moving by inertia*; as a result the bead resists and exerts an inertial force on the stick (exactly like when a particle away from gravitating masses moving by inertia is prevented from its inertial motion, it exerts an inertial force on the obstacle and the kinetic energy of the particle is converted into heat).

It appears more adequate if one talks about inertial, not kinetic, energy, because what is converted into heat (as in the sticky bead argument) is the energy corresponding to the work done by the inertial force (and it turns out that that energy, originating from the inertial force, is equal to the kinetic energy [9]). The need to talk about the adequate *inertial*, not kinetic, energy is clearly seen in the explanation of the sticky bead argument above – initially (before the arrival of the gravitational wave) the bead is at *rest* and *does not possess kinetic energy*; when the gravitational wave arrives, the bead starts to move but ** by inertia (non-resistantly)** since the shape of its

I would like to stress it that it is a fact in the rigorous structure of general relativity that gravitational waves do not carry gravitational energy, which, however, had been inexplicably ignored, despite that Eddington explained it clearly in his comprehensive treatise on the mathematical foundations of general relativity *The Mathematical Theory of Relativity* 2nd ed. (Cambridge University Press, Cambridge 1924), p. 248 [10]: “The gravitational waves constitute a genuine disturbance of space-time, but their energy, represented by the pseudo-tensor t^{\nu}_{\mu}, is regarded as an analytical fiction” (it cannot be regarded as an energy of any kind for the well-known reason that “It is not a tensor-density and it can be made to vanish at any point by suitably choosing the coordinates; we do not associate it with any absolute feature of world-structure” *ibid*, p. 136).

A systematic critical examination of standard arguments for the received view that gravitational waves carry energy-momentum is found in P. Duerr (Oriel College & Philosophy of Physics, Oxford): “Do Gravitational Waves Carry Energy-Momentum: Critique of a Procrustean Practice”, http://philsci-archive.pitt.edu/11857 (preprint).

**References**

1. 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) [9] 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.”

2. The geodesic hypothesis is regarded as “a natural generalization of Newton’s first law” [3], that is, “a mere extension of Galileo’s law of inertia to curved spacetime” [4]. 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.

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

4. W. Rindler, R*elativity: Special, General, and Cosmological* (Oxford University Press, Oxford 2001) p. 178.

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

6. The original prediction of gravitational wave emission, obtained by Einstein (*Berlin. Sitzungsberichte*, 1916, p. 688; 1918, p. 154), correctly identified the source of such waves – a spinning rod, or any rotating material bound together by cohesive force. None of the particles of such rotating material (except the centre of rotation) are geodesic worldlines in spacetime and, naturally, such particles will emit gravitational waves. This is not the case with double stars; as the stars are modelled as point masses, their worldliness are geodesics (which means that the stars are regarded as * moving by inertia*) and no gravitational waves are emitted.

7. An immediate and misleading reaction “A wave that carries * no* energy?!” should be resisted, because it is from the old times of three-dimensional thinking – assuming that a wave really

8. Sticky bead argument, https://en.wikipedia.org/wiki/Sticky_bead_argument

9. V. Petkov, “On Inertial Forces, Inertial Energy and the Origin of Inertia,” published as Appendix B in V. Petkov, *Inertia and Gravitation: From Aristotle’s Natural Motion to Geodesic Worldlines in Curved Spacetime* (Minkowski Institute Press, Montreal 2012).

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

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Louis Vervoort, 10.02.2016

*Minkowski Institute, Montreal, Canada*

In recent articles [1-3], three research teams, led by Anton Zeilinger at the University of Vienna, Austria [1], Lynden Shalm at NIST in Boulder, Colorado [2], and Ronald Hanson at the Delft University of Technology in the Netherlands [3] have reported on the untimely death of local realism. These teams have succeeded in the experimental *tour-de-force* to close, in a Bell experiment, the most relevant loopholes for local hidden-variable theories. ‘Realism’ is ‘the assumption that objects have physical properties independent of measurement’, and ‘locality’ is the assumption that there are no influences traveling faster than the velocity of light [1]. The general content of these publications is thus that one of these cornerstones of physics must be given up. If true, such a conclusion would surely represent a landmark in our intellectual history. However, I believe this conclusion is quite premature.

Upon closer inspection the authors appear to be more cautious. In fact, it appears that only a *certain class* of hidden-variable theories is eliminated by the experiments. Ref. [1] is maybe most explicit, by describing how the experiment would close the ‘freedom-of-choice’ loophole: “This loophole can be closed only under specific assumptions about the origin of [the hidden variables]. Under the assumption that [the hidden variables] are created with the particles to be measured, an experiment in which the settings are generated independently at the measurement stations and spacelike separated from the creation of the particles closes the loophole.”

Now, it is certainly very natural to consider the hidden variables as ‘pertaining’ only to the particle pair, more generally as created at the source with the particles, in the sense of [1]. But it is not the only possibility that is allowed by logic and physical law. My point is that the class of hidden-variable theories still exploiting the freedom-of-choice loophole is vast and natural. For instance, the hidden variables could, besides the particles, also describe a background field or medium in which the particles move and that interacts with particles and analyzers. In this case the full dynamics of the hidden variables is crucial, as I have recently investigated in detail in Ref. [4] (the background field may refer to vacuum fluctuations, an ether, a dark field,…). In [4] it is shown that such background-based theories can reproduce the quantum correlation of the Bell experiment.

Background-based hidden-variable theories are inspired by spectacular recent experiments by Couder, Fort, Bush and co-workers, which demonstrate that background fields (or pilot waves if one prefers) can lead to a surprisingly wide range of quantum-like phenomena in fluid mechanical systems [5-6]. Such background-based theories therefore remind one of Louis de Broglie’s pilot-wave theory. There is a whole series of physicists working on modern variants of this theory, attempting to derive quantum mechanics from a deeper level. One can also refer here to the Cellular Automaton Theory of quantum mechanics of Nobel Laureate Gerard ‘t Hooft [7].

In conclusion, the crucial experiments [1-3] do eliminate a wide and natural class of local-realistic models. But when more general claims are made (‘By closing the freedom-of-choice loophole […] we reduce the possible local-realist explanations to truly exotic hypotheses’ [1]), I disagree. There is a wide and natural class of local-realist theories that is not eliminated by [1-3]. Not only is local realism far from dead; I believe that by prematurely proclaiming its passing one has closed a promising road to finally reconcile quantum mechanics and relativity theory. Some more info can be found in [8].

*Acknowledgements. I thank Ronald Hanson for his kind willingness to discuss his group’s experiment and its interpretation*.

[1] M. Giustina et al., ‘Significant-loophole-free test of Bell’s theorem with entangled photons’, Phys. Rev. Lett. **115**, 250401 (2015)

[2] L. Shalm et al., ‘Strong loophole-free test of local realism’, Phys. Rev. Lett. **115**, 250402 (2015)

[3] B. Hensen et al., ‘Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers’, Nature **526**, 682 (2015)

[4] L. Vervoort, ‘No-go theorems face background-based theories for quantum mechanics’, Found. Physics **45**, 1 (2015), doi: 10.1007/s10701-015-9973-7

[5] A. Eddi, J. Moukhtar, S. Perrard, E. Fort, and Y. Couder, ‘Level-Splitting at a macroscopic scale’, Phys. Rev. Lett. **108**, 264503 (2012)

[6] J. Bush, ‘The new wave of pilot-wave theory’, Phys. Today, Aug. 2015, 47

[7] G. ‘t Hooft, ‘Models on the boundary between classical and quantum mechanics’, Phil. Trans. R. Soc. **A 373**, 20140236 (2015)

[8] L. Vervoort, Comment on ‘Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons’, arXiv preprint, http://arxiv.org/abs/1602.01859 (2016)

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*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 a 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 a 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 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*.

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*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].

**References**

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, R*elativity: 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).

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