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 of 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.

Now let us proceed. The sixth part
happens in

**GRAVITY
VERSUS/AND QUANTUMNESS, PART 6**

**FALSE
DAWN, ****HUNGARY****, OTL, 1985**

B. Lukács

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

H-1525 Bp. 114. Pf. 49,

lukacs@rmki.kfki.hu

**ABSTRACT**

Successes
in the second half of the 80's. Newtonian Quantum Gravity is at last
formulated even in OTL.

**0. ON FALSE DAWNS**

False dawn is a
meteorological phenomenon which seems as if it were
dawn, maybe it is dawn, but it is not followed by morning; or at least not for
a long time. I can mention 3 kinds of well known false dawns.

The first is a
peculiar light of sky at the end of some nights. It is not dawn; not yet. But
it is always followed by dawn; sooner or later. At least, always was followed
so far.

The second kind is the
False Dawn on Mercury [1]. Mercury's rotational and orbital periods are in 2:3 resonance. For first approximation this would mean simply
that 1 day = 2 years. However the orbit is highly eccentric. Therefore there
are latitudes where Sun first starts to peep in at the horizon, but then he
turns back. This is a false dawn. After some time he again starts; and then
goes up and there will be daylight for a Mercury year.

The third kind happens
at specific Terrestrial points. Maurus Jókai, famous although now forgotten
(abroad) Hungarian novellist depicts the usual
scenario at the industrial town Torockó (

Anything may happen. A
white dwarf is a dying star. Now, a brown dwarf is a star born already dying.

**1. A QUEST FOR NEWTONIAN
QUANTUM GRAVITY**

Not too much happened
between 1974 & 1985 about Quantum Gravity in *no* experiment was performed.

An Italian group
started something fundamentally similar to Jánossy's
idea (see Part 5) but much better elaborated. I mention here the names Ghirardi, Rimini, Weber & Grassi, and give a reference from amongst many as an
example [4].

And then the
Relativity Group of CRIP obtained some money by which it was able to organise
the first Hungarian Relativity Workshop (now we are at the sixth), called then
the Balatonszéplak Relativity Workshop. It was small,
but really international; and it was a chance for poor Hungarian physicists to
propagate their ideas. (Hungarian currency was not convertible to *any* other currencies, which was a
barrier against Conference participations. Interestingly, Hungarian currency
was *nearest* to free conversion in the

In order to make use
of the occasion, *three* Hungarian
lectures were made about *three*
different Quantum Gravity approaches, as follows here:

*Károlyházy*. A brief recapitulation of the model mentioned in Part 5,
General Relativity + Quantum Mechanics, plus the newest evolution of the theory
(that was [3]). This lecture is [5].

*Diósi**, Lukács,
Martinás & Paál*.
This was General Relativity + Quantum Field Theory, attacked from *thermodynamic* viewpoint. You take the
Universe. Its geometry is time-dependent, so you cannot do anything else than
to solve QED on a changing manifold, so a Hawking radiation of second kind
appears [6]. However this radiation *does
not seem objectively existing*, e.g. it does not
show Doppler shift between observers of relative velocities. This may be simply
a contradiction between the partial unifications **(G+c)** and **( h+c)**, but may be "real"
as well, since it may be the influence of the changing geometry

*L. Diósi & B. Lukács*.
Now, this Ref. [9] was a pure (**G**+** h**) approach, in
the way told in Part 2. What would happen if we

The next Chapter
summarizes this approach.

**2. QUANTUM GRAVITY WITHOUT
RELATIVITY**

Now I continue where I
chopped the story at Padraig O'Gallaghan
** in
ATL 1932**. But this is our OTL. I of course remember a lot, and I have
our conference lecture from 1985 [9]; but I would rather not ask my coauthor, and the whole thing happened 20 years ago, so in
minor details I may remember erroneously. However surely, I knew Károlyházy's theory well enough to calculate in it, and Diósi was interested in Measurement problem in Quantum
Mechanics. Now, if Gravity Reduces the wave function, then She Reduces only
macro objects, which is good.

As you see, I
calculated real experimental situations in the Károlyházy
model; Diósi did it too, but they were not published.
(As far as I remember, he calculated the noises from microearthquakes,
and you can imagine how vague the results might have been.) But he knew the model well enough. In addition he had the opinion
that the Measurement means a stochastic process acting
on the wave function [10]. Then ** Micro** is a system (having a coherent
Ψ) where this new stochastic term is negligible, and

Now, Jánossy's idea was that there is a new Law of Nature,
reducing when Ψ extends *too* *big*. Say, everything is reduced whose Ψ
extends on a region >R_{red}; then we can collect experimental
bounds for R_{red}, e.g. highly excited H atoms are inflated enough,
still Schrödinger equation reproduces the measured spectrum well, so the new
term does not yet operate [11]. And so on. Similarly, in the Ghirardi-Rimini-Weber scenario some extra laws determine
Reduction; such theories improve Quantum Mechanics, without *unifying* it with something.

As for the stochastic
description Diósi was up to date with models, Markovian processes and whatnot. And we were already
working together in 3 problems, one I mentioned in the previous Chapter,
another was the Riemannian structure of the *thermodynamic*
state space, and the third the very early Universe at the spontaneous breakdown
of the SU(5) symmetry of GUT. So why not a fourth; he presented me a “philosophical”
problem.

It was something
similar to the problem of Copernicus (I mean, for structure, not for
importance). Copernicus started from the observation (known for every
astronomer after Claudius Ptolemy, to be sure) that planets move on independent
epicycles, still the directional vectors of the first epicyclic cycles are *all*
parallel. Why? You cannot expect this from the Ptolemaic model, and such an
accidental coincidence is contrary to Occam's Razor. It must have a fundamental reason; he suggested that
these first epicycles are just the mirror images of Earth's cycle.

Now, in Károlyházy's theory light velocity ** c** plays important and fundamental
role, but c

Then I suggested the
scenario "If Einstein got encephalitis...".
The result became [9]. We got exactly Károlyházy's
Micro/Macro border even if light velocity appeared nowhere at all in the
theory. The recapitulation of the essence of [9] deserves a separate Chapter;
unfortunately 1985 is practically pre-PC Age in

**3. SHARP GRAVITATIONAL
POTENTIALS ARE MEANINGLESS CONSTRUCTIONS**

There are only G and ~~h~~
as fundamental constants of universal phenomena. (No Einstein, no Relativity.) There are two fundamental
theories, closed, excellent, but both of them neglect the other. The first is *both* constants.

Namely, let us assume
that we want to measure the gravity potential Φ(**r**). The simplest way is to hurl compact pebbles, and observe their
paths by telescopes. The equation of motion is

md^{2}**r**/dt^{2} = -mgrad Φ(**r**) (1)

Now, m drops out (which in itself is interesting, but is a fact). So
observing the path (also in time), the gradient of Φ is measured, and
thence Φ can be integrated, up to a constant, which is simply the freedom
in the zero point of energy.

However the stones we
hurl obey Quantum Mechanics. Take the simplest possible stones without
excitable internal structure and such. The stones have, of course, masses M and
sizes R. Their wave functions extend on a length L. It is not important if the
stones are all alike or not.

Obviously we cannot
measure Φ(**r**) on scales <L,
because we do not know where the stone "is". Surely we can prepare
arbitrarily sharp Ψ, so there is no lower limit to L. Also, we may
restrict ourselves to situations L<R. The observation goes until time T.
Then we in fact measure a space and time average of acceleration g (which is
-grad Φ). So:

<g>_{V,T} = (1/VT)∫g((x+ξ,t+τ)d^{3}ξdτ

ξ < L, V = 4πL^{3}/3 (2)

-T/2 < τ < T/2

The measurement goes for time T, during which the *change* of the momentum is p. Then

<g> = p/MT (3)

If we can measure <g> for arbitrarily small T and
L, then we are ready.

For this, however, we
should start with very small L. But

δ_{1}<g> ~ ~~h~~/MTL (4)

since

Lδp ~ ~~h~~ (5)

That is, we cannot start with too small L. Or, we can, but only if M is
big enough. Namely, L doubles in time

t_{2} ~ ML^{2}/~~h~~ (6)

Good; can then the sharp value of the acceleration g be measured by
means of pebbles of infinitely large masses?

No. The pebble is also
the source of the potential. Were we to know the exact position of the (center of mass of the) pebble, we could extract its
contribution from **g**; but we have a
position uncertainty L. The acceleration uncertainty hence is

δ_{2}<g> ~ GM/L^{2} (7)

(My proof here is somewhat simplified; I have assumed that the
averaging goes just to the interval L. We could average on areas >L too.
They give even worse results.)

The total uncertainty

δ<g> ~ {(~~h~~/MTL)^{2} + (GM/L^{2})^{2}}^{1/2} (8)

This diverges if T->0; if T is not small, we cannot measure sharp *instantaneous* values. Also, it diverges
if L->0. The smallest uncertainty is achieved with pebbles

M_{opt} ~ (~~h~~R/GT)^{1}^{/2}, L ~ R (9)

and then

δ_{opt}<g>
~ (~~h~~G/VT)^{1/2} (10)

This uncertainty is
inevitable; there is no way around. We can measure very sharply averages for
large domains and times; but there is *no
sharp instantaneous measurement* for the acceleration or for the gravity
potential.

In Quantum Mechanics
we accepted in the 20's that the fact that p and x cannot be measured simultaneously
sharply means that p and x are no c-numbers, but operators; and only their
averages or expectation values can be expressed via c-numbers. Now the
inevitable lower bound for the inaccuracy of the gravity potential must mean
something analogous. We shall see what, in the next Chapter.

**4. STOCHASTIC POTENTIAL**

Let us now write
simply

Φ = <Φ> + δΦ (11)

where <Φ> is simply
the old c-number solution of

<δΦ>
= 0 (12)

<δ^{2}Φ> = ~~h~~G/VT (13)

Obviously one cannot
go beyond (12-13) without at least a *model*;
results (12-13) state that Newtonian Gravity and Quantum Mechanics hurt each
other and that how much they are inconsistent. Obviously for Measurement
Problem Ψ should be stochastic [10]; if the energy operator in
Schrödinger's Equation is stochastic, then Ψ is stochastic via that
equation; and the energy operator is stochastic if Φ is stochastic. So let
us write

δΦ
= Φ_{sto} (14)

However from (12-13) we do not yet know the full
stochastic behaviour. Still, the *simplest
choice*, that Φ_{sto} is a *white noise*, works [12], and then

<Φ_{sto}(x,t)Φ_{sto}(X',t')>
= C~~h~~Gδ^{(3)}(x-x')δ(t-t') (15)

where C is a number constant of order
1, simply collecting all the neglected 2's and π's
in the above calculations. I am too lazy to evaluate them, so I write
henceforth C=1.

But then we can *determine*, where is
the transition zone between Micro and Macro physices.
Namely, let us rewrite the Schrödinger equation as

i~~h~~dΨ/dt
= E_{kin} + E_{sto} = (-~~h~~^{2}/2m)ΔΨ
+ MΦ_{sto}Ψ (16)

Now, order of magnitude estimations give for a wave packet of width
L~R:

E_{kin} ~ ~~h~~^{2}/MR^{2},
E_{sto} ~ M(~~h~~G/RT)^{1/2} (17)

For L>R the body is practically point-like; for L<R we must
somehow average up for the body, which is possible but will be ignored here.

If the kinetic term
dominates, the body approximately evolves as its center
of mass; this is the case of Classical Mechanics. However, if the stochastic
term dominates, then the behaviour cannot even approximately be represented by
means of unstochastic expectation values. This is
Quantum Mechanics. If *none* dominates,
then we arrive at unknown behaviours; at a region where Physics cannot be
guessed from the two partial theories known until now.

Now, this region of
new behaviour is then around

M^{3}R ~ ~~h~~^{2}/G (18)

In principle we cannot yet know the behaviour there, because we do not
yet have the Unified but Newtonian Quantum Gravity. Still, a first model is
available: Stochastic Gravity and Continuous Measurement. Diósi
elaborated a handy formalism for Continuous Measurement, and then everything
can be evaluated in the model. Unfortunately, he made a tactical error.

Eq.
(18) is the same as in Károlyházy's theory. (Cannot
be anything else; as I told above, we started from the observation that Károlyházy's Micro/Macro border formula does not contain ** c**
at all. From

In 1989 the situation
was as follows. Károlyházy was a Doctor of Science
since 1974, full professor, and what you like; at the *deliberately*, but tried
Heavy Ion Physics. I did not have enemies in Heavy Ion Physics, e.g. HIP
community was not interested in Quantum Gravity honours.

Then we looked after
the difference between Diósi & Lukács and the nonrelativistic
limit of the Károlyházy model; and we found it. It is
explicitly and very diplomatically written in [14]; we definitely did *not* write that one condition for
reduction is rather strange there; we only wrote that then the spectrum of the
stochastic fluctuations is *not* that
of white noise, and a white noise spectrum is more "attractive". But
even this was too much.

Namely in 1990 Diósi got the idea to write Theses too. He might have
chosen Thermodynamics, and then the history I narrate here would have been OK.
But he chose Continuous Measurement.

Now, the process
includes 3 opponents who must not work at the same institution as the
candidate. In this case that meant practically opponents from the *any* of
his questions). Of course the voting process and the argumentation was secret, but it took 21/2 hours instead of the usual 1/2,
so you can imagine what happened. I was angry and Diósi
was angry & hurt. The honour of the opponent theory was defended in a
definitely feudal manner.

Then we threw
discretion to the winds, and evaluated two realistic situations in the Károlyházy model. They are [15] & [16]; the titles are
explicit enough, I only add that in [15] we showed that the improbable
reduction condition would result also in strange celestial mechanics and in
[16] that lethal X-ray radiation would emerge from laboratory lead bricks. So
the condition cannot be correct. QED.

By the way, there was
some symbolism in the choice of journals too. [12] was
sent to Annalen der Physik, because Einstein's famous papers were published
there, and [15] was sent to Nuovo Cimento,
because Károlyházy's very first Quantum Gravity paper
was published there.

Diósi
wrote a string of papers about Measurement, density matrices, Markovian processes and Itoh
formalism, sent some letters to foreign colleagues, got more citations, and
defended his Theses in 1998. However then already political climate did not
favour our collaboration; if you do not understand this understatement, read
again Part 3 for analogy.

However we are really
still at the beginning of the 1990's. Two things happened, important to
Newtonian Quantum Gravity. First, in 1990 multiparty democracy returned to

Then we wrote the
paper; it is [17]. I stop here; the Spurious Scattering deserves a new Part of
its own. I close this part with recording that in 1994, when our project
financially ended, we (I mean, Diósi & I)
organised from the remaining money a very moderate Workshop where everybody
participated who was working in Quantum Gravity, excepting Penrose. There was a
Spurious Scattering lecture, [18]. And nobody defended [19] against [15] &
[16].

**6. OUTLOOK**

It still looked like a
True Dawn.

**REFERENCES**

[1]

[2] M. Jókai: Egy
az Isten.
(The title means: God Is One; that is the slogan of Unitarians, sometimes
called Modern Arians, who refuse Trinity. I do not know if the novel had
English edition at all.)

[3] F. Károlyházy, A. Frenkel & B. Lukács: On the
Possibility of Observing the Eventual Breakdown of the Superposition Principle.
In: Physics As Natural Philosophy, ed. by A. Shimony &
H. Feshbach, MIT Press, Cambridge Mass. 1982, p. 204

[4] G. C. Ghirardi, A. Rimini & T. Weber: Unified Dynamics for Microscopic and
Macroscopic Systems. Phys. Rev. **D34**,
470 (1986)

[5] F. Károlyházy: Gravitation and the
Breakdown of the Superposition Principle. In: Proc. Balatonszéplak
Relativity Workshop, 1985, ed. B. Lukács, p. 63

[6] G. W. Gibbons & S. Hawking: Cosmological Event Horizons,
Thermodynamics and Particle Creation. Phys. Rev. **D15**, 2738 (1977)

[7] L. Diósi, B. Lukács,
K. Martinás & G. Paál:
Thermodynamic Analysis of the Vacuum. In: Proc. Balatonszéplak
Relativity Workshop, 1985, ed. B. Lukács, p. 73

[8] L. Diósi, B. Lukács,
K. Martinás & G. Paál:
Thermodynamics of the Vacuum. Astroph. Space Sci. **122**, 371 (1986)

[9] L. Diósi & B. Lukács: Newtonian Quantum Gravity. In: Proc. Balatonszéplak Relativity Workshop, 1985, ed. B. Lukács, p. 95

[10] L. Diósi:
Gravitation and the Quantummechanical Localisation of
Macroobjects. Phys. Lett. **112A**, 288 (1985)

[11] L. Jánossy:
The Physical Aspects of the Wave-Particle Problem. Acta
Phys. Hung. **1**, 423 (1952)

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

[13] F. Károlyházy,
A. Frenkel & B. Lukács:
On the Possible Role of Gravity in the Reduction of the Wave Function. In: Quantum Concepts in Space and Time, ed.
by R. Penrose & C. J. Isham, Clarendon Press,

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

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

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

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

[18] 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,

[19] F. Károlyházy:
Gravitáció és makroszkópikus
testek kvantummechanikája. Magy. Fiz. Foly. **XXII**, 23 (1974)

Part 3: Hungary, 1918-19, OTL/ATL.

Part 6: 1985, OTL. ---You are here.

Part 7: 1990, experiments, OTL.

**My HomePage, with some other studies**, if you are curious.