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 first part is up to 1905, just a hundred years ago.

 

 

GRAVITY VERSUS/AND QUANTUMNESS, PART 1

 

FROM THE BEGINNING TO 1905

 

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

 

 

ABSTRACT

A bird’s eye overview is given about the Three Fundamental & Universal Theories of Physics,  namely Gravitation, Quantumness & Relativity. The final goal would, of course, be some unification, but at this moment even understanding the problem is something.

 

1. PREHISTORY

            Prehistory belongs to Philosophy, or perhaps to History of Science. For me, Egyptian priests of Heliupolis belong as well to Prehistory as the Great Ionian Forerunners. Water is not Everything although Thales might have told so; and it is hard (or too easy?) to get ideas for Unification from such teachings.

            It is tempting to make here a large bibliography to show that Elders conjectured something (or, really, that I know a lot about them). But I am too modest/lazy. So let us make a compromise: if I know this, I know a lot similar too, but then you do not have to read the bibliography. So: "Old Egyptians" knew about the sphericity of Earth. That is clearly Gravity; is it not?

            So let us see Diogenes Laertius from IIIrd century AD [8]. In Chapter 7 of his Introduction he writes: "...They consider that the world had a beginning and will have an end, and that is a sphere...".

            If you tell that it is too general a statement and it is not clear, what is "World" here, you are right. But then I continue. There is an old commonplace of Egyptian cosmography. 3 gods are involved: the God of Earth, male, Geb, the God of Atmosphere, Su, male, and the Goddess of Sky, Nut, female. Originally Nut lied on Geb, as proper for archparents, but then Su was born, and later he separated them. Now Geb lies supine, while Nut stands cow-like on all fours above. A frequent picture in graves; the Sky above Earth.

            But a Late Kingdom papyrus about 900 BC [9] depicts Geb as He forms an almost complete circle, His legs nearing His head. Is it not the pictorial formulation of the idea mentioned by Diogenes Laertius?

            I could mention other such ideas too, but I restrain myself.

 

2. ARISTOTLE, FIRST SCIENTIST

            I think, it is enough to start with Aristotle. Before him everybody is either a poet, or a philosopher, or at least we have no texts enough to decide. His teacher, Platon, has enough texts, and we can decide that he was not a scientist; philosopher at best.

            Now, Aristotle has physically clear ideas about Gravity. They are wrong, of course; Newton's ones are wrong as well. You can read Aristotle about Gravity in Phisica [10]. The theory goes as follows.

            Gravity is a phenomenon, depending on space and matter. As for space, it has a symmetry SO(3), it has one and only one Center, and acts on the line to the center. As for strength, no final statement is found in the extant texts (some 1/4 of the original).

            As for signature, observe that Aristotle works with 5 elements, whose gravitational sequence is Earth < Water < Quintessence < Air < Fire. For Earth Gravity is strongly attractive, for Water it is weaker, for Quintessence its action is nil, for Air it is weakly repulsive and for Fire it is strongly such. Therefore World is layered. The parts nearest to Center are full with strongly attracted Earth particles, and that is the body of Earth, spherical. Above there is a (narrow) layer of Water.

            You would expect inert Quintessence, but you find Air. I think, you should read On Generation and Corruption to understand this [10]. Aristotle's texts show that he wanted to continue his works, so not everything was his final word about. So there comes Air above Water, and Fire above Air; and then Quintessence. Milky Way is still in the Fire region, but near to its upper boundary. Meteors are phenomena from the Air-Fire boundary.

            Now I offer an explanation, as one Gravity researcher instead of another. Maybe Quintessence is anywhere, but not densely. Being gravitationally inert, it does not have to concentrate anywhere. However it is rather difficult to detect it if any of the other four dominates. Very far from Center only rare Quintessence is found, and being gravitationally inert, it will neither be attracted, nor repulsed by Center, so (this special typeface will go instead of long and possibly erroneous derivations for any theories) they will circle about Center. They are the "Celestial Bodies".

            That is quite a theory for 330 BC. It is not quantitative enough to predict comet recurrences (but there comets are meteorological phenomena near to the Air-Fire boundary) neither to predict the Eighth Planet Uranus (which is visible by naked eye), or the asteroids between Ares and Zeus (which are not), but these were not predicted either by Newton. In Aristotle's theory Gravity is not a force but a natural state of motion depending on space; it is not far from the ideas of General Relativity, which latter, however, will be out of the scope of the present series.

            This was the view of Peripatetics & Scholastics up to Galileo on Gravity. Concurrent views were worse. As for Quantumness, we vaguely can turn to atomistic ideas, expressing the idea that "things" are "quantized". Logics led to the idea that some grainy structure must be under "at the final structure". Practically no observation was cited. Aristotle was not against, but was rather sceptical.

 

3. NEWTON

            We can pinpoint the Theory of Gravitation of Newton to c. 1687 as the book [11]. Mathematically-minded authors would consider the gist of it as the 1/r² Law; but according to my view the Equivalence Law is more important. Namely, from Classical Greek times it was known that the distance of Moon is cca. 60 terrestrial radii. (Sorry, according to Indo-European consequtio temporum I should write that "it was known that ... it was". However still it is. My language is not Indo-European.)

            If so, Moon's orbital velocity is cca. 1 km/s. Now, observe an orbital path just overhead. Continuation of the original path would show away from Center, while fall would bring it towards. From Galileo's measurements we know the amount of fall, so orbital velocity just overhead is cca. 7.9 km/s. This means that

              (v₁/v₂)² = r₂/r₁                                                                                                             (1)

and the 1/r² force law comes hence. But any other power law would be as good; the important thing is that the same Gravity explains terrestrial ballistics and orbits of celestial bodies, with the same coupling. While exact equivalence will be something interesting enough to look for until c. 1900, it is experimentally true for first approximation since Newton. So Gravity is a fundamental phenomenon acting on everything; in some time Cavendish will measure the unique G.

            We will remain at the form of the Law of Gravity as formulated by Newton. (We shall see why.) However we will append it by the measurements of Eötvös (started in the 1890's), showing indeed the independence of matter up to many orders of magnitude, so probably exactly.

            Quantized viewpoints were rather foreign to Newton. Still, he considered light the shower of light particles (which we may properly call photons by pseudo-Greek lingo). His contemporary, Huyghens, considered light fundamentally a wave pattern, and from 1905 this will be the picture behind Quantum Physics, so we can mention a Double Nature here.

            I do not know if Newton ever calculated the deflection of a light ray just touching Sun; I am sure that it was not observed. However the idea is simple. At total solar eclipse you observe two stars just at diagonal perimeters of dark Sun. You get them at angular distance F - 2 df. Then you look for the two stars 6 months later in night, when Sun is not near to the rays. Then you measure F.

            Now, df comes rom Gravity. Light velocity is very high; denote it by c. The mass of a photon is unknown and small, but it cancels in the equation of the path, because it is linear on both sides of the equation of motion. All solutions of the 2-body problem are conical sections, for high velocities hyperbolas, and then you can exactly calculate the angle between incoming & outgoing asymptotics. This angle is

              df = 2GM/Rc²                                                                                                                       (2)

M is the solar mass, you know it from Newton's Gravity Law, + orbits of planets. R is Sun's radius, you know it from Sun's distance and its apparent size. For the velocity of light, Römer found c~308000 km/s, good enough. Writing everything into eq. (2) you get

              df = 0.83"                                                                                                                             (3)

small enough, maybe unmeasurable until photography.

            However Huyghens' prediction would be different,

              df = 0"                                                                                                                                  (4)

Namely, "waves do not fall". As an analogy, consider sound waves. If you start a sound wave obliquely, many things can happen, depending on the changes of elastic parameters of air on height. However a sound front starting horizontally will travel horizontally.

            So, maybe, light deflection measurements could decide. Unfortunately df is rather small.

            Anything written in this Chapter remains practically the same until 1900.

 

4. 1900: THE BIRTH OF QUANTUM PHYSICS

            About 1890 it turned out that something was ununderstood about Blackbody Spectrum. I will write this story elsewhere, but Blackbody Spectrum was produces by Nothing, namely by the empty interior of a dull but reflecting sphere. The measuring apparatus is the Ostwald (or Ulbricht) Sphere: a metallic sphere with rough interior surface (to scatter into all direction). If you make a small enough hole on the shell and place an oblique mirror behind to prevent direct reflection from the walls, and then you start to excite the Ostwald Sphere (by heating up, or by putting light into it, and waiting enough for equilibration), then you will see the Blackbody Spectrum.

            But Blackbody Spectrum has a unique form (as can be expected), however with a parameter T, which is the temperature of the system. Let us write it as the energy output between frequencies n and n + dn is

              dE = Vf(n;T)dn                                                                                                                      (5)

The V dependence is trivial.

            But then the dimension of f is ergs/cm³. Now, it would be easy to get

              f_RJ ~ Tn²/c³                                                                                                                            (6)

(RJ standing for Rayleigh & Jeans, who indeed published that approach in 1900) from the assumption that the electromagnetic radiation exists between almost infinitely conducting metallic walls (which is true in the Ostwald Sphere). The problem is that the total intensity, the integral of f from 0 to ∞ is infinite for any power law, which cannot be true, and f does not have a maximum, which is not true.

            Several attempts were made. Without claiming completeness, the Wonder Boy (really) of Hungarian astronomy, geophysics & meteorology (he explained the ages of some biblical patriarchs after Methuselah but before Joseph via the gestation cycle of ewes, which is almost exactly 5 months, and now check it!) started with interaction between Matter and Luminiferous Ether [12], thence measured Sun's surface temperature, and, look, it is quite good. Wien, not informed about Kövesligethy's book, used a semiempirical approach [13]. Using detailed Thermodynamics + Electromagnetism (including Doppler shift on moving pistons) he came to the formula

              f(n;T) = n³*H(T/n)                                                                                                                 (7)

where H(T/n) remained free. You can see that H(x)=x leads to the (wrong) Rayleigh-Jeans Law. He observed an exponential cutoff for large frequencies, so simply chose

              H(x) = exp(-b x)                                                                                                                    (8)

and got quite satisfactory results with b ~ 10^-27 ergs.

            In 4 years it turned out that he was incorrect. However even in 1896 he should have observed a problem.

            Obviously H(x) cannot be a power function; if it were, f(n) would be also a power function with infinite total energy. But anything not a power function must depend solely on a dimensionless argument!

            To demonstrate this, try to make a Taylor expansion of H(x). Different terms are of different powers, but must have the same dimension, otherwise you cannot sum them up. (Maybe you first think I forgot something. I really did not. The argumentation is OK. Think about the Taylor expansion of the exponential function of Wien if you are happy with the Royal Way of a particular proof.) But T/n is not dimensionless!

            OK, but b*T/n is such. Good; but what is b? Clearly a phyical constant, quite fundamental belonging to the empty interiors of spheres. OK, but whose theory's constant? Clearly not of Electromagnetism; that is c. Which theory is responsible for Nothing?

            It was not a problem in Kövesligethy's theory [12]. A constant may belong to Ether, permeating anything. But in the semiempirical approach of Wien?

 

5. 14TH DECEMBER 1900

            On 19th Oct. 1900 Planck recognised that up to measurement errors of Kurlbaum & Rubens the blackbody spectrum is compatible with the simple enough law

              H(x) ~ x*exp(-b*T/x)                                                                                                            (9)

and not with the choice (8) of Wien. As for derivation, it was simply the harmonic mean of two approximations, so nothing fundamental. However to 14th December he was able to derive his H(x) from a physical postulate: that energy is taken and given in integer multiples of portions (quanta = quantities) E=2pn/b [14]. In today's notation this is simply

              E_o = 2phn                                                                                                                              (10)

Since this seemed to be true for any interaction of atomic systems, from this moment Physics is Quantized, although it took a few years to be sure about.

 

6. MARITY, 1905

            I am sure the result mentioned in this Chapter comes in substantial part from Mileva Marity (this is the correct orthography, see the gravestone), born in Titel, Bács-Bodrog County, Hungary, 1875. Of course I do not deny the partial authorship of Albert Einstein (born in Ulm, Schwabenland, , Germany, 1879), not being feminist, but for later purposes I do not emphasize that here. I definitely detect the young lady's thermodynamic language in Article [15], and if Einstein never had been born (or had got an encephalitis while young), surely Mileva would have tried to catch Marcel Grossmann (born at Budapest, Hungary, 1878, interested in Non-Euclidean Geometries, and co-author of the first General Relativity paper [16] in Our Timeline) at the Technical Hochschule and written papers with him.

            The idea is simple enough about photons. There is a phenomenon called photoelectricity. Use alkali plates, best is caesium. If light falls on the plate electrons emerge and they close a circuit. Americans use it for opening doors of department stores when a consumer approaches.

            Now, a first approximation explanation is easy enough. (Remember, I speak, or rather Mileva speaks, from 1905). Electrons are known since 1897. Sometimes they easily take energy and leave the metal. It is most easily done in higher alkali metals. So indeed caesium must be good.

            Also, metals are good conductors, so the electron must not belong to individual atoms but rather to the whole lattice. So caesium lattices contain some weakly bound electrons, let the bound be DE for one electron. If the incident energy is concentrated on a single electron, then this electron leaves the lattice when taking DE energy.

            However concentration is a tricky business. The lattice will rather distribute the energy equally to all electrons. So the simplest prediction would be: for weak light a measurable time is needed for the first electron, later the lattice is "heated up", so the emergences are almost continuous. For weaker and weaker light you get longer and longer initial intervals; the frequency of light is not too important.

            However the experience radically differs. There is practically no initial delay, but weaker light results in lower flux. And frequency is crucial: below a critical frequency there is no electron emergence. At higher frequencies the kinetic energies of individual electrons roughly follow the law:

              E_kin = 2phn - A                                                                                                                      (11)

Here A does depend on the actual metal, and smallest for caesium, so caesium can produce electrons for the smallest frequency, even in near infrared. (So the consumer does not see anything at all.) But h is that of Planck (OK, I am anachronistic in notation; then everybody used hº2ph), so it is the same for all metals.

            It just seems as if electrons were meeting with individual energy packages of E=2phn, not of dispersed energy. So indeed these units do not belong to processes of energy input & output, but these quanta seem to be present even in the space far from atoms.

            They are the photons. Clearly there arises a problem. Light must be wave, because it clearly has frequency & wavelength, diffraction patterns can easily be formed & so on. So light is continuous. But clearly it is quantized as well. So light has a Double Nature.

            Then the two different results of light deflections at Sun, mentioned in Chap. 3 can be obtained too; which is the correct one? Astronomical technique became just appropriate to measure 1" by photography at telescopes, but this belongs to post-1905. For any case Quantization should be understood.

 

7. OUTLOOK; ALTERNATIVE TIMELINE

            For purposes understood after 1926 I will argue in the following 3 parts as if Relativity had not been formulated until at least 1926. This was not so impossible as you could believe. If Einstein had not made it, the Poincaré version surely would not have seemed so fundamental; maybe a sophisticated version of the Lorentz Transformation. And remember that in those years Abraham calculated a different, not relativistic, mass increase formula for electrons; and for a while it seemed conform to measurements.

            Really the true Physical Laws are independent of History. But the laws in which we believe are not. So let us go to an Alternative World, where Einstein did not go to the Technical Hochschule, and Relativity, as a Fundamental Theory, is not complete for one more generation.

            ATL and OTL start to diverge in 1896, latest, because Einstein is not at Zürich. Maybe, as I told, Marity catches Grossmann. She definitely did not want to discuss Luminiferous Ether and Electromagnetism of Moving Bodies even with Einstein in OTL [17]; but in later years she would have worked in Thermodynamics, and Grossmann, of course, in Bolyai-Lobatschewsky Geometry. First World War would have been exactly as on Our TimeLine; relativistic effects appear at the end of the Second, so maybe the War on Pacific would have ended in 1947 after bloody battles for the Japanese islands. But Relativity Theory did not influence the start of the war.

            In the next sequel I continue to the end of World War I. Some thermodynamic results of Einstein I will give to Marity, while some not very relativistic results (not correct anyways) about light propagation around Sun I will treat as works of obscure authors.

            After a few more parts you will understand this strange presentation.

 

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]       C. D. Yonge (ed.): The Lives and Opinions of Eminent Philosophers, by Diogenes Laertius. H. G. Bohn, London, 1853

 [9]       British Museum Papyrus 10,018

[10]      Aristotle of Stageira: The Complete Works. Ed. by J. Barnes. Princeton University Press, Princeton, 1995

[11]      I. Newton: De Mundi systemate liber Isacii Newtoni. J. Conduitt, London, 1728

[12]      R. von Kövesligethy: Grundzüge einer theoretischen Spektralanalyse, H. W. Schmidt, Halle, 1890

[13]      W. Wien: Über die Energievertheilung in Emissionsspektrum eines schwartyen Körpers. Annln. Phys. 58, 662 (1896)

[14]      M. Planck: The Theory of the Energy Distribution of the Blackbody Spectrum. Verh. der Deutschen Phys. Gesellschaft 2, 237 (1900)

[15]      A. Einstein: Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annln. Phys. 17, 132 (1905)

[16]      A. Einstein & M. Grossmann: Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. Z. Mathem. Phys. 62, 225 (1913)

[17]      A. Einstein & Mileva Maric: The Love Letters. Eds. J. Renn & R. Schulmann. Princeton University Press, Princeton, 1992. Look especially at the sequence of Letters 8-13 (from 14 to 25 there is no Luminiferous Ether at all). Letter 8, E to M, mentions the Electrodynamics of Moving Bodies; in Letter 9, M to E, there is no answer at all on that while Thermodynamics is briefly mentioned. Then in Letter 10, E to M, Einstein means Luminiferous Ether. Then he writes something which is proof that he tried to discuss this with Marity, but she did not react. ("But enough of this! Your poor little head is already crammed full of other people's hobby horses..."). Now, it happened many times that I was enthusiastic about an idea but my coauthor did not want to discuss; even ladies. I also tried a few times; then stopped. It seems that the answer is not extant, but surely nothing on Luminiferous Ether; in Letter 11, E to M, Einstein repeats the mention of Luminiferous Ether, albeit not in Letter 12 (there he writes about thermoelectricity and latent heat; and in Letter 13 Marity answers; but nothing about Luminiferous Ether. In some much later letters Einstein still tries; no reaction.