To our present knowledge (but there is little doubt about) both Gravity and Quantumness are fundamental and general phenomena, meaning that their laws govern anything & everything. (The third such is Relativity, and as far as we know any further is at best such a general philosophy as e.g. Causality.) But Gravity and Quantumness, as well in their old forms as in the present best ones contradict each other.

          But General Laws of Physics must not contradict each other. So if they contradict, they are incorrect. (At least one of them; but most probably both.) Very probably the way out would be Unification. Gravity & Relativity contradicted each other until 1916; then Einstein unified them, and the unified theory, General Relativity, is free of at least self-contradiction. Similarly, Relativity and Quantumness contradicted each other, but then they were unified c. 1947 as Quantum Field Theory. The unification was gradual, with such names as Dirac, Tomonaga &c., and the present status is a matter of argumentation. QFT does give infinities; but in some cases they are renormalisable, i.e. the infinities "can be removed". Also a lot of Field Theories, quite respectable in nonrelativistic limit, are unrenormalisable. Now this may mean that QFT is an erroneous Unification; but also that Relativity rules out the unrenormalisable Field Theories. This latter is the opinion of the overwhelming majority of QFT experts; and it may quite be correct. Anyways, Relativity rules out an acceleration to FTL velocities, and this "prediction" is generally accepted (with some sad feeling) by physicists.

          Quantumness and Gravity are also in contradiction in their original forms (as I told), but up to now the unification is not ready. The need of it and the reasons why it has not been made are the topics of this series (which will be being unfold or in Latin simply evolving gradually in several steps. The main reason to write these sequences is Advertisement; either of my own or of my viewpoint about. My feeling is that we are not far from the unification (see e.g. Refs. [1]-[7]), but surely we are not yet ready.

          I must state that (Unified) Quantum Gravity is/will be not the (Final?) Theory of Everything. The latter (sought by many, claimed by few and made by none so far) would be a Unification of Gravity, Quantumness & Relativity, a theory containing 3 fundamental constants, G, h & c, in a theory free of self-contradiction. I am less ambitious (more realistic?) for looking the third and last dual Unification, a Theory of G & h. You will see that it is a task enough in itself: and it would have quite enough new predictions in itself.

          At References for some articles I give  English translation. This does not happen if I am able to reach the original.

          Now let us proceed. The  fourth part is the advent of Quantum Mechanics in ATL.

 

 

 

 

 

GRAVITY VERSUS/AND QUANTUMNESS, PART 4

 

QUANTUM MECHANICS IS BEING MANUFACTURED; JUST AFTER WORLD WAR I. ATL/OTL

 

 

B. Lukács

 

CRIP RMKI, Theory Dept., & President of Matter Evolution Subcommittee of HAS

 

H-1525 Bp. 114. Pf. 49, Budapest Hungary

 

lukacs@rmki.kfki.hu

 

            ATL is the standard abbreviation of Alternative TimeLine, while our one, which certainly exists, is OTL. ATL's are visualized as diverging from ours at different key events; or we branched from another one, the difference is mere philosophy. ATL is a trick in Science Fiction, maybe the seminal novel was [8]; but not only there. The Alternative Quantum Mechanics of Everett [9] tells that at QM Measurements there is no reduction to one eigenfunction, but rather Reality splits, all the possible result of the Measurement realise "somewhere", and the histories continue independently. So all the alternatives are real "in some sense".

            There may be very many ATL's. The actual one diverged just before 1896, when Albert Einstein did not go to the Technische Hochschule of Zürich (or possibly to any University as student in Physics). If you want, you can think of encefalitis. It was not infrequent in that time, and even if the patient survived, he was not fit for University.

            To clarify my opinion, this would be a catastrophe for Physics. But it might have happened easily.

            For a while, for Quantum Mechanics, this ATL goes very similarly to OTL; maybe a bit faster, because Einstein's stubborn comments against Statistics in the Depth of Physics ("God does not throw dice") are absent. The very first Quantum Mechanical papers do not cite Einstein in OTL, as you can see it. World War I seems to have been quite independent of Einstein's existence. Although in OTL he seems to have been antimilitarist from childhood, his public peace activity started after the War; and his results had not been utilized.

            However, again, comments will be made from OTL.

 

ABSTRACT

Dirac, Heisenberg, Schrödinger & von Neumann formulate ATL Quantum Mechanics almost exactly as in OTL. But in ATL there is not yet Relativity (although somebody may formulate it soon; but not yet). So the incompatibility of  Newton’s Gravity & Quantum Mechanics is easily recognised in ATL.

 

1. INTRODUCTION

            As in OTL, Germany lost the War, but her research potentials are intact. The same is true for Lesser Austria. Hungary is full with promising researchers, but there is some problem about competition. E.g. it is not necessary to make research at Universities; and there are very few Research Institutes. E.g. Pekár, a protagonist of Part 3 and devout follower of Eötvös inherits his posts as Department Head and Member of Academy of Sciences in 1922, when his most serious publication is an Annalen der Physik paper about Eötvös's torsion pendulum measurement with Eötvös (already died) & Fekete [10].

            Do not misunderstand me. That paper is very important, see [11] from 1986 and a lot of papers in subsequent years. But look at the paper itself, and then you may detect that Eötvös got the idea, organised everything, and the others simply measured. (Or in Budapest lingo, with a Yiddish word and Budapest pronunciation, Eötvös was the Ezessgehber.)

            So Hungary drops out of the competition in Quantum Physics, and her Class A physicists often go to Germany. Also, the 1918-19 internecine struggle continues, even at Universities. The apparent reasons are formulated in various slogans; the true reason is that Hungary lost 2/3 of her territory and 1/2 of her population, so the poor State cannot support as many State employees as before.

            Until the War the victors had not been too interested in Quantum Physics (except for English Moseley, deceased really for the Tsar of Russia). Now they also will participate. I ignore de Broglie, because French is a difficult language.

 

2. ON THE DUAL ORIGIN OF QUANTUM MECHANICS

            The Quantum Mechanics starts twice (but within a year) and is the work of cca. 4 geniuses, who are all the New Generation. You will see it from the data of birth.

            Bavarian W. Heisenberg was born in 1901. Austrian E. Schrödinger was born in 1887. English P. A. M. Dirac was born in 1902, and Hungarian J. Neumann in 1903. The oldest of them was 13 at the discovery of Planck, and both Heisenberg and Dirac was confronted from the problems just at University (and Neumann was not confronted at all).

            Heisenberg's idea is to look for observables and their connections. This is Matrix Mechanics. He publishes the first complete results in 1925 [12]. Dirac operates with operators, eigenvectors & eigenvalues [13]. Then comes Schrödinger, shows that the two previous approaches are equivalent, and gives his formalism, which is Wave Mechanics [14] in 1926. Finally comes Neumann, and explains to all physicists what are they doing and how it could be done [15]. (A familiar viewpoint of mathematicians, indeed.) Neumann does this once more, when, in 1932, he fixes the axioms of Measurement [16]. We will return thither in due course.

            Let us follow the synthesis, and in specific formalism Schrödinger. In Newtonian Mechanics the physical quantity is a function (say, of time). But now it is an operator, while "Reality", the State is a function. Of course, the actual value of the quantity is a number, and then it is the eigenvalue of the operator when acting on State.

            Of course, generally the eigenvalues of the operator are more than one, so in the general State you cannot be quite sure, which value you will measure. There is even a Theorem of Uncertainty Principle that generally the values of 2 operators cannot be measured synchronously without "uncertainty", and for canonically conjugate quantities

              dA*dB ≥ h/2                                                                                                                         (1)

This follows from the existence of operators, but Heisenberg gives some visualizations as well. E.g. try to observe the location and the momentum of a particle simultaneously. The photon would kick the particle, so the momentum is  disturbed by the measurement itself. Then you would like to use a "very soft" infrared photon; but, alas, it is of long wavelength, so you will have a big uncertainty in location. The two "errors" are in inverse relation.

            So it seems that Quantum Physics contains an inherent stochastic component, some Indeterminism. Namely, if e.g. Energy is not unique in a state, then how could Energy Conservation be fulfilled exactly? Maybe it holds only in statistical average.

            But it is not so. State (the Y function of Schrödinger) evolves exactly causally and in fully determined way, fulfilling the Schrödinger equation:

              HY = [-h²Δ + V]Y = ih(d/dt)Y                                                                                              (2)

(H being the Hamilton operator), which is, indeed, a usual evolution equation. In stationary cases the right hand side is simply E*Y. No stochastic evolution at all.

            Until Measurement, says Neumann [16]. At measurement the quantum system is coupled to a macroscopic system and then the microscopic H operator cannot develop the micro system.

            Now, anything might happen then, but from experience physicists had some guesses, the guesses were formalised by Neumann, and the formalism "was good", by meaning that in manageable cases predictions and observations of the measurement process agreed. The idea is as follows:

            1) You have a Y in the actual state, and you want to measure the quantity Y.

            2) You must take the operator of Y; let it be Y.

            3) You then expand Y according to the eigenfunctions of operator Y; let us call the (generally full & orthonormalised) set of eigenfunctions & eigenvalues as {Y_i;Y_i}.

            4) The expansion is then unique:

              Y = ∑_i c_iY_i                                                                                                                            (3)

where the c's are complex numbers.

            5) Then the probability that you measure Y_k is

              p_k = c_kc^*_k                                                                                                                               (4)

            6) After Measurement Y is sharply in State Y_k ("Reduction of the Wave Function"), and then evolves hence.

            So indeed: Stochasticity appears with Measurement.

 

3. BEYOND QUANTUM MECHANICS

            This is the ATL situation in 1932. Then in Germany comes Hitler, and lots of physicists go to Great Britain, Ireland and USA, as in OTL. (So in ATL Ph. Lénárd, Pressburg, Hungary, 1862 does not scandalise himself with pro-Nazi speeches, because in OTL he made them because he was unable to understand Relativity at all.) We can guess that the next step will not happen in Germany where ideas are not free anymore. It will happen neither in Hungary, where University professors are interested only in keeping their positions and teach new ideas of somebodies else. Maybe not even in Austria, occupied by Germany in 1938. From OTL I do not see ATL clearly, but I think the place finally would be Ireland. Ireland has not quite linear or not quite left-hemispheric logics, and that is good to Unify Theories.

            Namely, not much after completing Quantum Mechanics (which is both in OTL and in ATL 1932, but of course in ATL there is not yet Dirac equation, being that relativistic, although Anderson detects positron in 1932, and discussions start about the strange mirror symmetry of Nature) somebody (for definiteness' sake let us call him Padraig O'Gallaghan) recognises that the two Fundamental Theories of 1932 mutually contradict to each other.

            Newton's Universal Gravity makes statements about Gravity Potential. If sources (mass distributions) are given, you can calculate the Gravity Potential, and hence Gravity Force. If the masses are not fixed, the Potential will act on them, and then the spatial distribution changes, but you can calculate the change, and then again the Potential. This is verified in Celestial Mechanics; you can calculate the motions of planets and the agreement with observations is excellent. True, there is an anomalous perihelion advance of Mercury. The observed value is 575"/century, of which the perturbations of other planets explain 532"/century, but 43"/century is a mystery [17]. (In the first calculation the discrepancy was rather 38”.) OK; maybe there are intra-Mercurial bodies [17], or if they cannot be seen, we can use Newcomb’s idea. Mercury is near to Sun. Maybe some rare atmosphere of Sun reaches Mercury's orbit and disturbs the motion. Maybe that gas is responsible for zodiacal light too.)

            But, notes O'Gallaghan, the masses generating Gravity Potential are not c-numbers, but q-numbers: there are Y's for them (in fact, for the Solar System there is a common Y of 31 variables). Then what about the resulting Gravity Potential? If its sources are not sharp, the Potential cannot be sharp either. Let us see if the naive way, to apply both Universal Theories simultaneously, can be done, or not.

            O'Gallaghan proceeds as follows...

 

4. BACK TO OTL

            I better switch back to OTL; ATL at the time of O'Gallaghan diverged some 40 years from OTL and I cannot see the details anymore.

            But, strangely enough, O'Gallaghan's idea was repeated in OTL Hungary some 50 years later, and there I know the details (although the work has not yet been finished).

            So we continue the discussion in OTL; Part 5 will be 1974.

 

REFERENCES

 [1]       L. Diósi & B. Lukács: In Favor of a Newtonian Quantum Gravity. Annln. Phys. 44, 488 (1987)

 [2]       L. Diósi & B. Lukács: On the Minimum Uncertainty of Space-Time Geodesics. Phys. Lett. A142, 331 (1989)

 [3]       Ágnes Holba & B. Lukács: Is the Anomalous Brownian Motion Seen in Emulsions? Acta Phys. Hung. 70, 121 (1991)

 [4]       L. Diósi & B. Lukács: Károlyházy's Quantum Space-Time Generates Neutron Star Density in Vacuum. Nuovo Cim. 108B, 1419 (1993)

 [5]       L. Diósi & B. Lukács: Calculations of X-Ray Signals from Károlyházy's Hazy Space-Time. Phys. Lett. A181, 366 (1993)

 [6]       Ágnes Holba & B. Lukács: Is the Spurious Scattering a Quantum Gravity Phenomenon?. in Stochastic Evolution of Quantum States in Open Systems and in Measurement Problems, eds. L. Diósi & B. Lukács. World Scientific, Singapore, 1994, p. 69

 [7]       B. Lukács: Triality in the Depth of Physics? On the Fundamental Unification. in Proc. 6th Symp. on Matter Evolution, eds. B. Lukács & al., KFKI-1995-21, p. 6. Also on Internet: http://www.rmki.kfki.hu/~lukacs/3DEPTH.htm

 [8]       L. Sprague de Camp: Lest Darkness Fall. Ballantine Books, New York, 1974 (but a shorter magazine version appeared back in 1939)

 [9]       H. Everett III: Relative State Formulation of Quantum Mechanics. Rev. Mod. Phys. 29, 454 (1957)  )

[10]      R. Eötvös, D. Pekár & E. Fekete: Beiträge zum Gesetze der Proportionalität von Trägheit vund Gravität. Annln. Phys. 68, 11 (1922)

[11]      E. Fishbach & al.: Reanalysis of the Eötvös Experiment. Phys. Rev. Lett. 56, 3 (1986)

[12]      W. Heisenberg: Über quantentheoretishe Umdeutung kinematischer und mechanischer Beziehungen. Z. f. Phys. 33, 879 (1925)

[13]      P. A. M. Dirac: The Fundamental Equations of Quantummechanics. Proc. Roy. Soc. Lond. 110A, 561 (1925)

[14]      E. Schrödinger: Quantisierung als Eigenwertproblem I. Annln. Phys. 79, 361 (1926)

[15]      J. von Neumann: Mathemathische Begründung der Quantenmechanik. Göttinger Nachr. 1, 1 (1927)

[16]      J. von Neumann: Mathematische Glundlagen der Quantenmechanik, Springer, Berlin, 1932. (There he notes that the part dealing with Measurement is a result of discussions with L. Szilárd. Szilárd was born in 1898, of course in Hungary. You cannot, of course, follow such a discussion because it goes on a Western Siberian, weakly polysynthetic language. Marity was weak in it, but Grossmann spoke it albeit his first language was German. (Note that Ref. [16] is not exactly the same in ATL & OTL. E.g. Footnotes 134, 145 (photon) & 184 (statistical meaning of Thermodynamics) cite Einstein in OTL and Grossmann-Marity and others in ATL.)

[17]      U. Le Verrier: Recherches sur l’orbite de Mercure et sur ses perturbations. Comptes Rendus 8, 273 (1843)