Gravitation: the most fundamental interaction
Johan Hansson* Division of Physics Lule˚aUniversityof Technology SE-971 87 Lule˚a,Sweden
Abstract The comprehensive analysis by Niels Bohr shows that the classical world is a necessary additional independent structure not derivable from quantum mechanics. The results of measurement must be ex- pressed classically; there must be a classical region of every experiment where physicists can set apparatus, read pointers and so on. As we will see, the events constituting spacetime of general relativity is this classical structure. Hence, gravitation is required to make the for- mal quantum mechanical coexistence of many mutually incompatible possibilities result in the concrete reality of the normal world, mak- ing gravitation the most fundamental interaction. It also means that “Quantum Gravity” is a pseudo-problem, a mirage, “Quantum Space- time” an oxymoron.
1 Gravitation presents the opportunity to connect, and resolve, two of the outstanding unsolved problems in fundamental physics: 1.) “Quantum Gravity” - that is, how quantum mechanics can be made to “peacefully coexist” with general relativity. 2.) “The Quantum Measurement Problem” - that is, how the ghostly co-existing superpositions of many mutually incompatible possibilities in the formalism of quantum mechanics - linear probability amplitudes - turn into the real world of concrete occurrences that we experience, even though both we and our measuring instruments are made of atoms described by quantum mechanics. From what we today know about nature a solution of the mea- surement problem must be nonlinear, to break quantum superposition1, and nonlocal, required by Bell’s theorem  and its numerous experimental tests , showing correlation of space-like separated events. Niels Bohr  emphasized that a classical framework is independently needed2 to connect purely formal quantum mechanics with observable facts, as observers and their measuring devices by necessity are classically real. “The primary unanalyzable reality of ordinary experience” is a necessary additional assumption and not something derivable from quantum mechan- ics. Bohr also said “there is no quantum world”, just an abstract quantum formalism to connect experiences in our real world - the only one. As John Wheeler asserts: “No elementary quantum phenomenon is a phenomenon until it is a registered (observed) phenomenon” . Furthermore, John Bell  showed that all measurements can be boiled down to positions; the position of instrument pointers, ink on a computer output, etc. But positions in space at given times are events - which are relativity. Wheeler also states “Happily, nature provides its own way to localize a point in spacetime, as Einstein was the ﬁrst to emphasize. Characterize the
1No amount of linear quantum “decoherence”  (quantum phase randomization), nei- ther internal nor environmental, can ever explain the disappearance of coexisting quantum possibilities ,  if everything, including measuring instruments and observers, are quan- tum entities. This is demonstrated very transparently in e.g. . Wigner , and also von Neumann , argues that the nonlinear collapse, ﬁnally allowing deﬁnite outcomes to be realized, happens when the consciousness of the observer (somehow) terminates the von Neumann-chain of ever larger linear superpositions. However, where and how does consciousness ﬁrst enter in the hierarchy of life (human/cat/cockroach/amoeba/.../God)? The problem is then just replaced by an even trickier one. 2A multitude of alternative “resolutions” of the quantum measurement problem have been proposed over the years, without succeeding.
2 point by what happens there! Give a point in spacetime the name “event”.”  - events are the invariant fundamental “atoms” of reality, the same for all observers, the point-manifold of which build up and constitute the totality of spacetime. Relativity is a classical theory in which events, and their rela- tionships given in terms of invariant spacetime intervals, are indispensable. Events are primary, the fundamental concept of observed nature. “Quantum Spacetime”? There is no such thing. The geodesics in curved spacetime are gravity, and they consist of classical events. (In a hypothetical gravitational-free world, or whenever gravity may be neglected for all practical purposes as in particle physics experiments, the geodesics are straight lines ↔ special relativity.) Several authors, e.g. ,  and many more, have linked gravity to the mechanism that turn mere subjective quantum mechanical “tendencies for possibilities” into cold, hard, classical facts - events. This is possible as general relativity is a truly nonlinear theory. The three other known funda- mental interactions, Quantum ElectroDynamics, Quantum FlavorDynamics (“the weak force”) and Quantum ChromoDynamics, are all purely quantum mechanical and as such powerless to classically realize their mere quantum potentialities and hence, by themselves, cannot generate a classical world. For example, a quark quantum ﬁeld is never detected, instead there are var- ious signals in a detector classically observed. Even though QFD and QCD are nonlinear (non-abelian), quantization3 linearizes them. The nonlocality of reality4 , , empirically validated , has a direct analogue in general relativity - the energy-momentum of the gravitational ﬁeld is not locally deﬁned - due to the equivalence principle it is always possible to choose local free-falling coordinates which makes gravity, locally, 5 µν evaporate . The generally covariant four-divergence T;ν = 0 is not a con- servation law but describes the exchange of energy and momentum between (local) matter with energy-momentum tensor T µν and (nonlocal) gravitation
3For example by inserting their “classical” action in the Feynman functional path- integral - “summing”, i.e. functionally integrating, over all ﬁeld histories - which is just a fancy description of linear quantum superposition of amplitudes. 4Bell’s theorem is not merely a statement about quantum mechanics but about nature itself, and will survive even if quantum mechanics is superseded by a more fundamental theory in the future. Although Bell used aspects of quantum theory in his original proof, the same results can be obtained without doing so. 5This also shows that localized gravity (e.g. gravitons), in terms of merely special relativistic Lorentz-covariant quantum ﬁeld theory, never can encapsulate all of gravity.
3 . Gravity is a global eﬀect, not a local one. Furthermore, the very origin of quantization is bound states6. Even in quantum mechanics a free particle can have any of a continuum of non- quantized energies - and in general relativity “test-particles” ﬂoat freely along geodesics as long as only gravity is at play7, disqualifying quantization. All said and done, this leads us to conclude that it is futile to expect that gravity should be quantized, as it would rob us of the classical world in terms of events absolutely crucial for making sense of quantum mechanics - and also crucial for making observations in the ﬁrst place (not to mention functioning as a social human being). Classical events are indispensable for the scien- tiﬁc endeavor, and as relativity is this spacetime of events it should not be quantized. Deterministic chaos can, and demonstrably does, exist in classi- cal mechanics as it is a theory of events which is nonlinear - the necessary criterion for chaos. Quantum-mechanically, chaos (e.g. extreme/exponential sensitivity to initial conditions) cannot exist, as quantum mechanics is a lin- ear theory about quantum amplitudes8. Through gravitation we can thus understand both why events occur at all, and why the measurement can lead to “randomness” - for all practical, but not fundamental, purposes, unlike the “magical” Born rule of wavefunction “collapse” where perfect random- ness is postulated a priori without any physical description, preventing any real understanding. Relativity is a theory of actualities, real occurrences, our very perceptions. Quantum mechanics, unless “measured” (giving events), is a theory of abstract possibilities we never have actual contact with. What is often missed is that quantum mechanics is just as deterministic as classi- cal mechanics, or even more so due to the simple linearity of its equations - which is required for quantum superposition to be possible. All the un- certainty, “randomness” and probabilities of “quantum mechanics” actually only appear in the (normally ill-deﬁned) “measurement” - producing classical events. 6Discrete bound states in atoms, for example, give quantized photons. And the very historical origin of quantum mechanics andh ¯ in the ﬁrst place - Planck’s resolution of the “black body” cavity radiation - is due to that the bound quantum harmonic oscillator can take on only energies in “packets”, i.e. quanta, ¯hω. 7The reason we feel gravity at all is because, e.g., the ﬂoor hinders the - for gravity - “natural” free-fall through spacetime, destroying geodesic motion by the non-gravitational electromagnetic interaction between body and ﬂoor. 8To obtain N bits of information regarding its future dynamics a chaotic system requires ∼ N bits of input information, a linear system only ∼ logN, validating Bohr’s insight that the classical world is independently needed.
4 Let us end with an analogy: In older television sets quantum mechanical electron beams are recorded as events on the screen, building up a compre- hensible moving picture pixel by pixel - it would be counterproductive, in fact ludicrous, to insist on having a “quantum screen” where all pixels are some- how lit at once in some sort of superposition in abstract inﬁnite-dimensional Hilbert-space 6= our living-room. Replace [TV screen] with [gravitation = collection of real observable spacetime events] and [[electron]] by [[formal abstract quantum entity]] and you get the gist of this whole article. To summarize: Quantum mechanics is about merely formal mathematical possibilities/potentialities - co-existing quantum amplitudes in some abstract space; relativity is about actualities - events in real spacetime. The transition [quantum amplitudes → events] is traditionally called “measurement”. Thus relativity cannot, and should not, be quantized as it is necessarily needed to both realize the mere possibilities of quantum mechanics, which it can do through the nonlinearity of general relativity which invalidates superposition, and provide the classical framework9 of Bohr necessary to make sense of quantum mechanics.
9This also means that the Planck-scale has no physical meaning. As ¯h → 0, as is appropriate as the spacetime of general relativity is merely a “book-keeping” of all realized classical events, the Planck-length/mass/energy/time/temperature all go to zero.
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