quant-ph0208048.tex
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{\LARGE\hfill       Superluminal transmission \hfill}



{\LARGE\hfill       is possible from now on\hfill}



{\vfill }



{\Large\hfill       Zbigniew Andrzej Nowacki\hfill}



{\vfill }



{\it\hfill       Computer Engineering Department, Technical University of Lodz,\hfill}



{\it\hfill       Al. Politechniki 11, 90$-$924 Lodz, Poland.\hfill}



{\tt\hfill       Fax: +48 606 560 005\hfill}



{\hfill       E-mail: nova@kis.p.lodz.pl\hfill}



{\vfill }



{\small 





     It is known that superluminal transmission of  information 
and energy contradicts Einstein's relativity. Here we  announce 
an  unusual  TOE  called 'nature theory'  in  which  impossible 
things  become possible. We present the scheme of an  apparatus 
for  sending  signals over arbitrarily  large  distances   with 
speeds  arbitrarily  exceeding  the  light  speed  in   vacuum. 
Introducing  the notions of effective speed and reliability  of 
superluminal  devices,  we encourage experimenters to  set  and 
break  world  records in this new branch. At the same  time  we 
outline a mechanism (termed 'particle encapsulation') owing  to 
which nature theory remains Lorentz invariant and so consistent 
with  experiments.  From among other numerous  applications  of 
nature theory we discuss briefly local antigravitation and  new 
computing  machines, called 'vacuum computers',  applying  'cat 
principle'.  They are of great interest because  should  enable 
humans to overcome the G\"{o}del-Turing barrier.}   


{\vfill }



{\bf\hfill       12 pages, 1 figure\hfill}



{\newpage}

     In  the  celebrated 1905 paper [1]  Einstein  changed  our 
approach to time and laid down a new foundation for all  modern 
physical  science.  One of the consequences of  his  theory  of 
relativity is that no signal or interaction can be  transmitted 
faster  than  $c$,  the  light speed in  vacuum.  But  since  the 
mid$-$1960s  physicists  have  been  carrying  out  a  number  of 
experiments   [2$-$16]  indirectly   demonstrating   superluminal 
activity  of Nature. As any competitive relativity  theory  has 
been  never  created,  and  all  physics  cannot  be   refuted, 
psychological (to some extent) barriers prevented experimenters 
and  referees from sending and considering useful  superluminal 
signals.   The  situation  was,  nonetheless,  disturbing,   so  
various  explanations  have  been proposed.  The  most  popular 
maintains  that  there is a fundamental  level  (heavens?)   at 
which, unlike the observational one (earth?), immediate signals 
can  be  sent  (by God being at rest?).  However,  a  connected 
theory of both the levels would have to use Galileo and Lorentz 
transformations simultaneously, which seems to be inconsistent.  
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\noindent \mbox{\bf Einstein antinomy}


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\noindent The  proof  of the superluminal transmission  impossibility  in 
special  relativity is well-known, but here we shall  need  its 
probabilistic  version. Suppose that we have an  apparatus  for 
sending  signals with a speed $c$\,+\,\(\epsilon \). It can be used,  according 
to  the relativity principle, by any inertial experimenter  and 
in  any  direction.  Similarly as every  physical  device,  our 
apparatus  need not be completely reliable. For simplicity,  we 
describe it by a probability matrix $p$\(_{ij}\), where $i$ equal to 1  or 
0  denotes correspondingly sending or not a signal, while  $j$  --- 
receiving  a  signal  or not in a time  interval  of  specified 
duration $T$. (Note that $p$\(_{i0}\)\,+\,$p$\(_{i1}\)\,=\,1.) We assume that 


\begin{description}\item \(\displaystyle\hfill          p_{01} < p_{11},  \hfill\)\end{description}
\noindent i.e., our device works at least somewhat. Suppose further  that 
an  experimenter  $E$  travels from (\mbox{\boldmath\(x\)},$s$) to  (\mbox{\boldmath\(y\)},$w$).  During  the 
journey  he  performs  an  experiment  whose  result  $X$  has  a 
probability $p$\(_{1}\) distinct from 0 and 1. Being at (\mbox{\boldmath\(y\)},$w$), $E$ sends a 
superluminal  signal  $S$ to (\mbox{\boldmath\(r\)},$t$) (rigorously speaking,  to  its 
neighborhood  with the time size $T$) if and only if $X$  has  been 
obtained.  By virtue of Lorentz transformations we  may  assume 
that  $E$\(^{\prime }\,\!\) (a human or computer) at (\mbox{\boldmath\(r\)}\(^{\prime }\,\!\),$t$\(^{\prime }\,\!\)) moves in such  a  way 
that 


\begin{description}\item \(\displaystyle\hfill          \mid \mbox{\boldmath\(x\)}^{\prime }\,\!\,-\,\mbox{\boldmath\(r\)}^{\prime }\,\!\mid \,\leq \,(s^{\prime }\,\! - t^{\prime }\,\!)(c + \epsilon ).                     \hfill\)(1)\end{description}
\noindent Thus  it  is possible that,  immediately after  getting  $S$,  $E$\(^{\prime }\,\!\) 
sends  a  superluminal signal $S$\(^{\prime }\,\!\) to (\mbox{\boldmath\(x\)}\(^{\prime }\,\!\),$s$\(^{\prime }\,\!\)).  Therefore,  if  $E$ 
receives  $S$\(^{\prime }\,\!\)  at (\mbox{\boldmath\(x\)},$s$), then he knows that the  probability  of 
obtaining $X$ in the starting experiment is equal to   


\begin{description}\item \(\displaystyle\hfill          p_{2} = \frac{p_{1}(p_{11}^{2}+p_{10}p_{01})}{p_{1}(p_{11}^{2}+p_{10}p_{01})+p_{0}p_{01}(p_{00}+p_{11})},\hfill\)\end{description}
\noindent where  $p$\(_{0}\)\,=\,1\,$-$\,$p$\(_{1}\).  The first contradiction consists  in  that 
$p$\(_{2}\)\,\(>\)\,$p$\(_{1}\).  Moreover, $E$ is clever. He substitutes $p$\(_{2}\) for  $p$\(_{1}\)  and 
gets  $p$\(_{3}\)  greater again. From continuity it follows  that  \{$p$\(_{n}\)\} 
converges  to  1. This signifies that  Einstein's  dream  comes 
true;  all  probabilities, quantum physics,  Las  Vegas,  etc., 
vanish.   Seriously   speaking,  we  have   proved   that   any 
superluminal  transmission,  even at  very  low  probabilities, 
refutes  special  relativity. And this blights hopes  that  the 
uncertainty of quantum phenomena can save Einsteinian  physics. 
We  see that quantum mechanics is at odds with it,  so  another 
relativity theory is needed. This task was very difficult,  but 
lately [17] it has been at last performed. 


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\noindent \mbox{\bf Superluminal technology}


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\noindent This is a historical moment, my reader. In Fig. 1. you may  see 
the  outline  of  the  first  official  apparatus  for  sending  
superluminal  signals,  a human activity that will  be,  in  my 
opinion,  common in the third millennium. To build  the  device 
you  need  nine mirrors (denoted by $M$),  three  beam  splitters 
(\mbox{\em BS}), two clocks ($C$), one laser ($L$), one photodetector ($D$), one 
computer  or at least button ($B$), two walls or beam  stops  ($W$) 
and, first of all, two similar nonlinear crystals (\mbox{\em DC}) able  to 
split   an  input  photon  into  two  output  ones  with   less 
frequencies (the so-called 'parametric down conversion'  [18]). 
The crystals should be optically pumped by a coherent pump wave 
emitted by $L$ and split at \mbox{\em BS}\(_{1}\). This can cause the conversion of 
input  photons at one or both crystals, each with the  emission 
of a signal particle $s$\(_{j}\) and an idler $i$\(_{j}\). 


     Consider  first the situation without the line from $C$\(_{1}\)  to 
\mbox{\em BS}\(_{2}\).   As  photon  paths  reaching  either  \mbox{\em BS}\(_{2}\)  or   \mbox{\em BS}\(_{3}\)   are 
indistinguishable, particles, no matter whether they have  been 
converted,  interfere.  This means that  the  remaining  dashed 
lines  are not used either. In particular, similarly as in  the 
usual  interferometer,  no photon (above the vacuum  level)  is 
registered  by  $D$.  Note that in this  phenomenon  there  is  a 
second-order  as  well as fourth-order interference,  but   the 
latter,  being  useless at superluminal  transmission,  is  not 
visible owing to the geometry of Fig. 1. 


     Now  suppose  that one of  experimenters  presses  (after, 
maybe, long hesitation) $B$. Then $C$\(_{1}\) records time and raises  (or 
lowers, knocks over, etc.) \mbox{\em BS}\(_{2}\), using, e.g., an  electromagnet. 
This causes that idler photons cease to interfere, and they are 
registered  by detectors having 100\% efficiency,  i.e.,  walls. 
But  this  enables one, in principle, to  determine  whether  a 
signal photon arriving at \mbox{\em BS}\(_{3}\) comes from \mbox{\em DC}\(_{1}\) or \mbox{\em DC}\(_{2}\).  (Applying 
beam  stops instead of walls can be more practical because  the 
absorption  should  occur  rather quickly  [17].)  Thus  signal 
particles  stop interfering as well, and about 50\% of them  can 
be recorded by $D$. (That the possibility of distinguishing idler 
photons  destroys the interference of signal ones was  verified 
experimentally  in a similar configuration [19].) Therefore,  a 
useful  signal has been sent from $B$ to $C$\(_{2}\). Indeed,  the  second 
experimenter  knows  that,  e.g., she has  been  asked  out  to 
dinner. 


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     \put(14,0){\small FIG. 1. The scheme of an apparatus for superluminal transmission of signals.} 


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     It remains to estimate the speed of this signal consisting 
of  all  the  three main types  of  particles:  tardyons  (here 
electrons  denoted by bold dash lines), luxons  (photons),  and 
tachyons. We assume, for simplicity, that for each $j$ the  sizes 
of  \mbox{\em DC}\(_{j}\) and the distances between $M$\(_{j1}\), $M$\(_{j2}\), and $M$\(_{j3}\) as well  as 
between  $W$  and \mbox{\em BS}\(_{2}\) are infinitesimal. Thus \mbox{\em DC}\(_{2}\), \mbox{\em BS}\(_{2}\),  and  \mbox{\em BS}\(_{3}\) 
constitute  a  right  triangle whose legs are  denoted  by,  of 
course,  $s$  and $i$. As letting idler photons pass  destroys  the 
interference of merely their partners, we get the maximal speed 


\begin{description}\item \(\displaystyle\hfill          v_{max} = \frac{c\sqrt{s^{2} + i^{2}}}{s - i}.\hfill\)\end{description}
\noindent Strictly  speaking, $v$\(_{max}\) is the speed of virtual tachyons  [17] 
carrying  a piece of information on raising \mbox{\em BS}\(_{2}\). It is easy  to 
see that $v$\(_{max}\) exceeds $c$ whenever 0\,\(<\)\,$i$\,\(<\)\,$s$. For example, in the 
geometry  of  Fig.  1. it equals $c\sqrt{5}$. Increasing  $i$  you  may 
obtain   greater   and  greater  speeds   (arbitrarily   large, 
theoretically),  but you should not reach or exceed $s$.  Indeed, 
no  particle,  even virtual, can move  with  the  infinitesimal 
speed  or backwards in time [17]. More precisely  speaking,  if 
$i$\,\(>\)\,$s$,  then  information can be transmitted rather from  $D$  to 
\mbox{\em BS}\(_{2}\),  while in the case of $s$\,=\,$i$ both the beam  splitters  work 
independently. Note, however, that the probability of the  last 
setting vanishes. 


     To  calculate  the minimal speed, denote by $T$\(_{0}\)  the  total 
time  of electronic parts except $B$, and --- by $T$ the entire  time 
of  raising  \mbox{\em BS}\(_{2}\).  As the reaction time of  $D$  depends  on  the 
difference  of radiant fluxes reaching it, we may  assume  that 
the  time  is  approximately equal to \mbox{\em kr}\(^{2}\)$/\!$$I$,  where  $r$  is  the 
distance  between \mbox{\em BS}\(_{1}\) and $M$\(_{1}\), and $I$ --- the intensity of $L$.  Thus 
we get 


\begin{description}\item \(\displaystyle\hfill          v_{min} = \frac{\sqrt{s^{2} + i^{2}}}{\frac{s - i}{c} + \frac{kr^{2}}{I} + T + T_{0}}.\hfill\)\end{description}
\noindent This  implies that a necessary condition for  the  superluminal 
transmission is




\begin{description}\item \(\displaystyle\hfill          r\sqrt{2} > cT_{0}.\hfill\)\end{description}
\noindent Therefore, increasing $r$ and $I$ you may start. Note that $T$ is not 
so  essential here because some signal photons can be  affected 
even when \mbox{\em BS}\(_{2}\) is raised only in part. To take advantage of this 
possibility you should use a statistical procedure. 


     Let a computer perform an experiment consisting of  cycles 
following  one another repeatedly, each of which  involves  two 
stages.  In  the  first stage (termed the  {\em action  period})  the 
electromagnet  begins to raise \mbox{\em BS}\(_{2}\), raises it  completely,  and 
finally  lowers  to the initial position. In the  second  stage 
(termed  the  {\em standby period}) \mbox{\em BS}\(_{2}\) is entirely lowered  all  the 
time.  The  duration $a$ of the action period is  fixed  for  all 
cycles,  while --- $s$ of the standby one is  increased  gradually. 
Let  $V$  be  a  positive  number, and  $w$  ---  a  nonnegative  one 
dependent,  in  general, on $V$. Denote by $Q$ be the  quantity  of 
alarms  raised during ($t$,$t$+$a$+$s$] excluding ($t$+$r$$/\!$$V$,$t$+$r$$/\!$$V$+$w$],  and 
by $Q$\(_{0}\) --- during ($t$,$t$+$r$$/\!$$V$], where $t$ is the initial instant of the 
cycle.  Suppose  that the averages of those quantities  in  all 
cycles  performed  so  far  are denoted  by  the  same  symbols 
correspondingly. Then by the \mbox{\em reliability} of the apparatus  with 
the transmission speed $V$ we mean 


\begin{description}\item \(\displaystyle\hfill          R(V) = 1 - \lim_{s\rightarrow \infty }\,\frac{Qr}{Q_{0}V(a+s-w)}\hfill\)\end{description}
\noindent provided $Q$ does not vanish. (Of course, in practice it suffices 
to increase $s$ merely to some ceiling.) The least upper bound of 
the set \{$V$: 0 \(<\)\,$R$($V$)\} is called the {\em effective speed} $v$\(_{eff}\) of the 
apparatus.  If we have $R$($V$)\,=\,1, then the device works at  this 
speed  perfectly.  The  reliability  equal  0  for  all  speeds 
signifies  that  it  operates in an  entirely  accidental  way, 
whereas a negative $R$($V$) --- that we should decrease $V$. 


     It  is recommended that in a session either $w$ vanishes  or 
$r$$/\!$$V$\,+\,$w$  for all examined $V$ is constant. The quantity  obtained 
in this way is termed the {\em waiting period}; in our case it may be 
set  to zero. However, the above statistical procedure  can  be 
equally well applied to assess other superluminal methods,  and 
then  $w$  will  be  able  to  be  essential.  We  believe   that 
experimenters,  especially  working  so  far  at   superluminal 
propagation but not only, will construct quickly the  apparatus 
of Fig. 1. or present other devices. It is easy to verify that 


\begin{description}\item \(\displaystyle\hfill          \frac{p_{01}(V)}{p_{11}(V)}\,\leq \,1 - R(V).  \hfill\)\end{description}
\noindent Therefore, to refute special relativity it suffices to transmit 
signals  with $v$\(_{eff}\) exceeding $c$, i.e., $R$($V$)\,\(>\)\,0 for some  $V$\,\(>\)\,$c$. 
We   think,   similarly  as  many   physicists   dealing   with 
superluminal propagation [15, 20], that this is certain. But do 
not  worry and be happy; in our opinion we may live in a  great 
palace instead of a hut.   


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\noindent \mbox{\bf Nature theory}


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\noindent The  approach presented in [17] has been called  {\em nature  theory} 
simply  because  its only model is the whole  Nature.  In  this 
theory  the  foregoing impossibility proof  (similarly  as  its 
standard version) is false and so termed 'Einstein's antinomy'. 
This signifies that the transmission of information and  energy 
over  arbitrarily  large  distances   with  speeds  arbitrarily 
exceeding  $c$ becomes admissible from now on. At the  same  time 
nature theory respects Lorentz transformations between inertial 
observers. This presentation makes it sound as if you could eat 
your cake and have it further, but that is a mathematical fact. 
Precisely speaking, we have proved Lorentz transformations with 
weak assumptions not causing contradictions. 


     It is worth pointing out that nature physics is the  third 
theory  using Lorentz transformations. Let us recall  that  the 
first of them, Lorentz's himself, was based on the aether,  and 
said how matter interacted with it.  The next, Einstein's,  was 
based  on the physical (homogeneous and isotropic)  space,  and 
dealt  with  interactions between matter  and  space-time.  The 
present  approach  [17] is based on the  vacuum,  and  involves 
solely  interactions between particles. This is possible  owing 
to the full quantization of the nature theory vacuum consisting 
of   virtual   particles.   They   were   known   of    quantum 
electrodynamics,  but in nature theory virtual  particles  have 
been  defined  in  a much more general and  perfect  way.  This 
causes that [17] is not only an alternative relativistic study, 
but  also  an  attempt at  explaining  quantum  phenomena,  too 
difficult  ---  as  he  himself  admitted  ---  for  Einstein.  For 
instance,  virtual particles enable us to carry out the  second 
quantization  of  wave (the first one was done  by  Planck  and 
Einstein).  As a result, we obtain, e.g., a causal  explanation 
of   the   double-slit  experiment  and   a   fully   objective 
wavefunction interpretation implying that of Born. We are  also 
in  a position to give an answer to Wheeler's recent  question: 
'How  come  the quantum?' It is, in our  opinion,  the  virtual 
particle   of   nature  theory,  the  least   object   existing 
physically. 


     Virtual  particles cannot be (for a reason following  from 
their  definition [17]) observed in a direct way. But  Fig.  1. 
shows that they can be included in signals and then affect  our 
real world. Therefore, we assume that every signal consists  of 
particles.  Now we are in a position to explain why  Einstein's 
impossibility  proof cannot be restored to nature theory.  This 
brilliant scholar recognized that two moving observers did  not 
experience  time and distances in the same way. But he did  not 
notice  (unhappily, for otherwise quantum physics would not  be 
such a problem for him [21]) that, aside from time dilation and 
length  contraction,  there was one more  relativistic  effect: 
particle encapsulation. It consists in that moving observers do 
not see exactly the same particles. This causes, in particular, 
that  if (1) holds, then $E$\(^{\prime }\,\!\) does not see, i.e., cannot  receive 
$S$. (Let us admit that it is easy to say: 'does not see',  while 
in  reality there are a lot of technical difficulties  overcome 
only in [17].) Thus the action of the device does not depend on 
sending  any  signal, that is, $p$\(_{01}\)\,=\,$p$\(_{11}\). Hence we  infer  that 
superluminal transmission does not lead to any  contradictions. 
Furthermore,  we have proved that if $O$ sends a signal, and  the 
relative speed of $O$ and $O$\(^{\prime }\,\!\) is sufficiently small, then $O$\(^{\prime }\,\!\)  will 
receive   this   signal.   This   ensures   that   superluminal 
transmission is physically feasible. 


     The apparatus presented in Fig. 1. is designed for sending 
information,   but  superluminal  transmission  of  energy   is 
possible as well, even though we have proved that by virtue  of 
Lorentz  transformations  the speeds of real  particles  cannot 
exceed  $c$. (This proof was lacking in Einsteinian  theory.)  To 
transmit  the  energy  of  real  particles,  they  have  to  be 
transformed  into a field energy. It is a property  of  virtual 
particles  (constituting  fields), so it can be sent  with  any 
speed. Finally, the energy is transformed into real particles.   


     Particle  encapsulation should not be any great  surprise. 
Indeed, it is slightly similar to to the so-called 'many-worlds 
interpretation  of  quantum mechanics'  [22$-$24].  However,  the 
encapsulation  causes branching rather particles  than  worlds. 
(We do not maintain that if you go to the cinema tonight,  then 
there  is another universe in which you will stay  home.)   And 
their  coalescence  is possible whenever the  danger  that  the 
experimenter  will  come  to know  own  future  disappears.  In 
particular,  there  is  no encapsulation  in  a  region  unless 
superluminal  signals are received in it; i.e.,  nature  theory 
contains special relativity. 


     It should be pointed out that our theory is local,  albeit 
in  the  most general sense of this word. This means  that  the 
behavior of a particle depends solely on particles being in its 
neighborhood.  Note  that  this  definition  does  not  exclude 
faster-than-$c$  interactions  and signals. Their speeds  in  our 
approach  are unbounded and finite, while according  to  Newton 
they  could be infinite, and according to Einstein they had  to 
be bounded. And somewhat surprisingly, nature theory is  causal 
and  indeterministic (as a younger sister of  quantum  physics)  
at the same time. We are in a position to explain exactly  what 
forces  real  particles  to act  in  an  indetermined  fashion. 
Nevertheless,  the postulates of nature theory may  be  changed 
under the influence of new experimental facts. Therefore, it is 
possible that in (rather distant) future our theory will become 
determined.  One thing is certain: Bell's inequalities [25]  do 
not stand in our way. 


\vspace{0.5\baselineskip}



\vspace{0.5\baselineskip}



\noindent \mbox{\bf Antigravitation}


\vspace{0.5\baselineskip}



\vspace{0.5\baselineskip}



\noindent There are three main application areas of nature theory:


\begin{itemize}\item  Superluminal transmission of information and energy.


\end{itemize}\begin{itemize}\item  Local and controllable antigravitation.


\end{itemize}\begin{itemize}\item  Vacuum computers.


\end{itemize}\noindent The  realization  of merely one of them can  change  our  life. 
Nonetheless,  if at least one of them has not been realized,  I 
will be the first to say that nature theory is unsuccessful. 


     Local   and   controllable   antigravitation   caused   by 
antimatter  explains the symmetry violation in decays  of  some 
particles  [26] and what we see through telescopes at the  sky. 
Of  course,  it  is  at  odds  with  Einstein's  principle   of 
equivalence,  but  is  consistent with  quantum  physics.  [17] 
demonstrates that we need not return to Newton's principle with 
its  accidental equality of gravitational and inertial mass  of 
particles belonging to matter. Instead, we have the fundamental 
postulate   of   nature  theory  called   the   controllability 
principle.  Owing  to  it we are able  to  distinguish  between 
gravitational   and   inertial  forces  by   means   of   local 
experiments,  and  at  the  same  time  there  is  exactly  one 
component  of  unified  charge, termed  mass,  responsible  for 
inertial,  gravitational,  and  even quantum  effects.  In  our 
approach Einstein's famous formula has to be replaced by 


\begin{description}\item \(\displaystyle\hfill          E = \mid m\mid c^{2}.\hfill\)\end{description}
\noindent Two vertical lines are essential here because the mass $m$ can be 
negative,  whereas the energy $E$ cannot (in nature  theory).  We 
predict that the antigravitational action of antimatter will be 
soon corroborated by experiments performed in CERN. 


\vspace{0.5\baselineskip}



\vspace{0.5\baselineskip}



\noindent \mbox{\bf Vacuum computers and cat principle} 


\vspace{0.5\baselineskip}



\vspace{0.5\baselineskip}



\noindent The  quantized vacuum of nature theory enables us to  introduce 
the  notion  of a vacuum computer. A bit of the RAM  memory  of 
semiconductor-based  machines  corresponds  to  an  excess   or 
shortage  of real electrons in a region. Analogously, a bit  of 
VAM  (Vacuum Access Memory) being used by vacuum  computers  is 
defined  via  a measure of virtual particles  with  a  definite 
unified  charge  being  in a region. There are  many  sorts  of 
vacuum  computers;  their logic gates can consist  of  real  or 
virtual  particles.  We  have proved [17] that  some  of  those 
machines will be able to compute non-recursive functions [27]. 


     Quark-vacuum  processors,  whose logic gates are  made  of 
virtual  quarks,  will be perhaps the most  excellent  machines 
constructed by humans at any time (whenever nature theory turns 
out  to  be  true).  Here the vacuum allows  one  to  omit  the 
Planck-Einstein  law  (stating  [17] that  there  are  at  most 
finitely    many    real   particles   crossing    a    bounded 
four-dimensional  region).  This  law  implies,  in  fact,  the 
Church-Turing  thesis [27], but it is not the sole obstacle  to 
computing  non-recursive  functions.  Note  that  even  if   an 
ordinary computer worked with an exponentially increased speed, 
it  could not perform any infinite calculation during a  finite 
time  for  a  simple reason: its hardware would  then  have  to 
remain in an indetermined (not being even random) state,  which 
is  physically impossible. That is why quark-vacuum  processors 
will  apply a mechanism called 'cat principle'. It says that  a 
bit  can be written and a logic gate can be used at most  once. 
Owing  to  it  some infinite calculations will be  able  to  be 
performed.  Indeed,  they will be reduced to  setting  physical 
fields in perfectly determined states. 


     A  few years ago the promising development  of  artificial 
intelligence  was  disturbed by publishing  [28].  As  people's 
dream  of constructing machines really thinking is so  winsome, 
Penrose's   book   has  been   repeatedly   being   criticized, 
misrepresented,   or   simply  left  unsaid.  But   facts   are 
implacable;  Penrose (refining Lucas' argumentation  [29])  has 
shown that no Turing-equivalent machine, even equipped with   a 
random  mechanism,  can exactly simulate the human  mind.  This 
involves  not only electronic or molecular [30]  computers  but 
quantum ones [31, 32] as well. Penrose's proof ought not to  be 
disregarded  because  it  is  based,  in  fact,  upon   G\"{o}del's 
incompleteness  theorem  [33]. A solution of  this  problem  is 
given  only  in nature theory; we have  proved  that  Penrose's 
reasoning does not embrace quark-vacuum processors. In reality, 
these beasts will be much better at thinking than humans.  Thus 
we  suggest  realizing  Hilbert's famous program  by  means  of 
physics (i.e., the consistency of mathematics would follow from 
that of Nature). Another potential application is  establishing 
the notion of truth in that portion of mathematics which  deals 
with  integers.  And --- last but not least --- no  planetoid  will 
threaten us. 


     One  may ask about the chance that those machines will  be 
built. Obviously, vacuum computers are related to quantum ones; 
in  both the cases one tries to use something existing  outside 
our   real  world.  However,  computer  science  has  been   an 
algorithmic  field  so far, while quantum  physics  commissions 
Nature  to perform difficult tasks without defining how she  is 
to  do them. Quantum physicists say apologetically that  nobody 
knows  how  Nature does it. In many cases this  is  now  false. 
Nature theory is an algorithmic science; nature theorists  know 
or  have  to  define  what Nature does, how  and  why.  So  far 
knowledge  --- and not its lack --- has been rewarded, and we  hope 
that this tendency will be continued. 


     We encourage you to read an introduction to nature  theory 
contained in [17], especially if you are a physicist,  computer 
scientist, or mathematician, but not only. You will find there, 
among  other things, the description of an  unusual  scientific 
conference that will be held about 3000. Invitations to it will 
be  very difficult of attainment, but everyone has still got  a 
chance. 








                        
\vspace{\baselineskip}\begin{center}ACKNOWLEDGMENTS
\end{center}






     I   thank  Prof.  D.  Sankowski  for  creating   excellent 
conditions to writing this article. 






                          
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