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\begin{document}
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\title{
\hbox to\hsize{\normalsize\rm Oct. 2002
\hfil Preprint MPI-PTh/2002-59}
\vskip 36pt
Presence On Earth of Non-Identical Particles}
\author{L.~Stodolsky}
\address{Max-Planck-Institut f\"ur Physik 
(Werner-Heisenberg-Institut),
F\"ohringer Ring 6, 80805 M\"unchen, Germany  
~~~~~~~~~~~~~~~~~~~~~~~~~~ email: les@mppmu.mpg.de}
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\maketitle
\bigskip




\begin{abstract} A change of 
physical constants with time could imply that
 particles reaching the earth in high energy cosmic rays from 
distant parts of the universe are different from local particles. 
Some speculations on the detection of such ``alieons'' are
presented.

\end{abstract}
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 At least since Dirac's ``large numbers'' paper~\cite{dirac}
there has been speculation about a possible time dependence of the
fundamental physical constants, a fascinating idea that
never  has been convincingly confirmed or refuted.
The discussion 
recently new impetus with the claim~\cite{claim}  that 
observations of high
redshift spectral lines  indicate a value of $\alpha$  (fine
structure constant)   differing from its earthbound value.
This has   stimulated  various theoretical
speculations~\cite{theo}.

In general we might expect two kinds of situations with
respect to time-varying physical pararmeters. In one, the values of
the constants would depend, say, on some kind of local field. Thus
independent of any history,  local properties are always the same.
This is as in general relativity.

Or, in another variant  the properties of a particle could depend
on
its history. For example, as seems plausible, the {\it rate} of
change of physical constants
could depend on local conditions. In this case the properties of a
particle 
could depend on the space-time path it used to reach us. In fact
 Weyl's original ``gauge invariance'',  
was rejected by Einstein for this very reason; an atom's
 spectral lines would depend on its history~\cite{weyl}.
We know from everyday experience that  such history-dependent
effects cannot be very large or very frequent. But it is perhaps
not
entirely excluded that they are present very weakly or very rarely.
While such a situation would open a Pandora's box of difficulties
involving such basic principles as gauge invariance and the
exclusion principle, it is perhaps amusing to briefly consider a
few of the consequences. 

In  particular  we would like to draw attention to the
interest of very high energy cosmic rays in this connection.
Very high energy cosmic rays  are believed to reach the earth from
remote parts of
the universe. In a
universe with time dependent physical parameters this could imply
that they arrive at the earth  with properties characteristic of
the region of their origin, different from those prevailing near
the earth.  
 


  For energies above the
``knee'' at $\sim 10^{16} eV $ in the cosmic ray spectrum, protons
and nuclei cannot
be contained by the magnetic field of the galaxy, and it is
believed that  these cosmic rays are of extragalactic origin. In
intergalactic space they travel essentially
freely and at these energies there is nothing to stop them coming 
to the earth
from great distances. Hence it is 
conceivable that  presently on the earth  there are a small number
of ``alien''~\cite{harald} particles --call then ``alieons'' --of
remote extragalactic origin.
 
A second point is the high velocity of these cosmic rays. With time
dependent constants, particles presumably undergo some kind of
``ageing'' process. If this is in some way as in  
 special relativity where, as is well known, fast relativistic
particles ``age'' more slowly (in the sense of their lifetime for
decay),  then alieons
would be very ``young''. The time dilatation factor for  a
$10^{16} eV$
proton $\gamma \approx 10^{7}$ means a high energy cosmic proton
that  has been travelling during the whole lifetime of the universe
 upon reaching us is only
about a thousand years ``old''. Naively, we
might then expect that  its properties have ``aged'' very little
compared to a local, stationary proton. Of course, without a
detailed theory we do not know how the ``ageing'' process takes
place nor if the time dilatation effect is not compensated by
perhaps some tensor property of the fields involved. However,  this
would seem very curious, ---in an admittedly already very curious
situation. 


The particles in questions are essentially
nucleons since protons and nuclei are the dominant
component of the high energy cosmic rays.
The rate of cosmic rays in the region of the ``knee'' is about one
per square meter per year. Multiplying  by the area of the earth's
surface and period of $1.2\cdot 10^{10}$ years we obtain  $\approx
6 \cdot 10^{24}$ as an
estimate
for the number of accumulated extragalactic particles,
corresponding to   about 0.01 grams for protons or 0.5 grams
for nuclei. This
is to be compared
with $6 \cdot 10^{27} g $ for the mass of the earth. Hence the
density of
alieons  could be on  the order of $10^{-28}-10^{-29}$ if they are
 uniformly distributed throughout  the earth. On the other
hand,
they might be concentrated, say, on the surface or in the oceans,
leading to a much higher density in certain materials or regions.
Alieon neutrons from  incoming cosmic ray nuclei may be of special
interest 
since after slowing down they can be captured and remain in 
nuclei.

 



With the suggested  non-standard value of $\alpha$, the most
striking property to look for
 would evidently
be protons of non-standard charge. These would presumably end up as
molecules that are not completely neutral. The
reported~\cite{claim}  anomaly for  $\alpha$,  on the order of
$10^{-5}$ is not very small. If straightforwardly turned into
a change of charge, that is without concern for what is happening
to c or $\hbar$,(--not to mention other factors--) and assuming
negligible
``ageing'' gives a change of charge
$\sim 10^{-2}-10^{-3}$.  Since the claim~\cite{claim} is for
a {\it reduced} value of  $\alpha$, a normally neutral atom or
molecule would have a slightly {\it negative} charge  $\sim (10^{-
2}-10^{-3})\times e$. Perhaps high-throughput chemical means or
molecular beam
methods could be used to concentrate and search for
 the ``alie-ocules''. By the
same token these systems (as well as their ions), although very
rare, would show distinct shifts of their spectral lines in the
laboratory.    

 A most dramatic aspect of  alieons would
be their escape from the exclusion principle~\cite{plaga}.
Having a
different value for some parameter such as charge, mass, or
magnetic moment,  an
``alieon'' would no longer be identical to its local counterparts,
and  the hamiltonian no longer a symmetric operator under
interchange 
of particles of the same species. Therefore, for example, the
wavefunction 
no longer need  be antisymmetric for  neutrons in a nucleus.
An alien neutron captured in a nucleus would not  remain
 near the top of the neutron fermi gas of the nucleus and would
fall to the bottom of the nuclear potential, much as a hyperon in
a hypernucleus. 
 The resulting object, an ``alietope'', would presumably be an
isotope differing in
mass from the local version by the  nuclear fermi energy, a few
tens of MeV.

Because of the  shift in nuclear energetics of the resulting
anomalous isotopes it is possible that certain  beta or electron
capture  
transitions, usually energetically forbidden, would become
possible. If these could be identified, low-background experiments
of the double-beta decay type might be entertained.

A potentially experimentally interesting signal in large detectors 
could  be the observation of the energy release in gamma rays as
the alien neutron transits to the bottom of the nuclear potential
well. However, unless the degree of non-identity is very small, 
this would seem to be a rapid process and most alien neutrons
should have transited long ago. The question may be handled in a
manner analogous to that of nuclear isospin, where at first
neutrons and protons are treated as  identical and then neutron-
proton differences lead to a breaking of ``identity''. That is, we
have a term in the
hamiltonian, {\it antisymmetric} in the exchange of a neutron and
an alieneutron,
proportional to $(\delta p )$ the  deviation of some parameter 
such as mass or magnetic moment from its usual value. We would
expect, very roughly, the rate of transition $\Gamma$ to be then
$\Gamma= (\delta p/p )^2 \Gamma_{0}$ where $\Gamma_{0}$
is the typical rate of  a nuclear radiative transition,
say~\cite{ww} $\sim
10^{-14} s$. Hence unless $(\delta p/p )^2 $ is very small the
alien neutrons should transit quickly.

Of course with a
 velocity-dependent ``ageing''  as mentioned above, we should
perhaps take into account that nucleons in the
nucleus, (or for that matter electrons in the atom) have a spectrum
of semi-relativistic velocities. If they were ageing at different
rates, there ought to be a gradual process of relative
``alienation'' with a slow continuous rate of Pauli principle
violating transitions.







 

Particles whose parameters  differ a ``little bit'' are of course
completely foreign to quantum field theory as we know it. All
copies of a given type of particle should be produced by
application of the one and the same field operator. A great
revision of theory would be necessary to deal with a situation
where this is not true. Especially, the presence of different
values of the fundamental charge $e$ in the same region of space-
time would necessitate substantial changes in our present
understanding
of gauge invariance.    
These questions  and many more which quickly come to mind are
symptomatic of the fundamental difficulties,-- but perhaps also new
vistas-- that would arise  should ``alieons'' exist.


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I am indebted Harald Fritzsch  for stimulating my interest in this
topic  and for 
 discussions on the above points, and to E.
Lorenz for a remark  on the interest of large detectors.


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%\section{Acknowledgments}

%I am indebted to
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\begin{references}

\bibitem{dirac} P. A. M. Dirac, Nature {\bf 192}, 235 (1937). 

\bibitem{claim} J.K. Webb, M.T. Murphy, V.V. Flambaum, V.A. Dzuba,
J.D. Barrow, C.W. Churchill, J.X. Prochaska, A.M. Wolfe, Phys. Rev.
Lett {\bf 87} 091301
(2001),
.

\bibitem{weyl} See section 65 of {\it Theory of Relativity}, by W.
Pauli, Pergamon Press. 

\bibitem{theo} X. Calmet and H. Fritzsch, Phys.Lett. B540 (2002)
173-178, ; H. Fritzsch, ; P. Langacker
G. Segre and M.J. Strassler, Phys Lett {\bf B 528} 121 (2002), and
further references in these papers.  

\bibitem{harald} I thank H. Fritzsch for the word
``aliens''.

\bibitem{plaga} The question of  violation of the Pauli principle
{\it per se}  has been considered over the years. See for example
R. Plaga Z.Phys. {\bf A333} 397,1989 and an  article by
E. Baron, R. Mohapatra, an V. Teplitz. Phys Rev. {\bf D59} 036003,
 which contains a short review of previous
literature.
The limits in these discussion seem to be far from the
 sensitivity  required by our estimates.  I stress that, unlike
these
papers, I do not question the validity of the Pauli principle for
truly identical particles. 

\bibitem{ww} See Fig 3.6 in {\it The Physical Theory of Neutron
Chain Reactors} by A. M. Weinberg and E.P. Wigner, Univ. of Chicago
Press.


\end{references}

\end{document}

 If it is indeed true, that like the decay lifetimes for particles,
relativistically moving objects ``age'' less rapidly, the above
considerations suggest a bizarre experiment. Let a beam of nuclei
be kept at a highly relativistic velocity in a storage ring for say
a year, at the end of which they will be a about a year ``younger''
than the surroundings. Inject these nuclei into a large detector
designed so that  their neutrons are captured  by nuclei in the
detector. Due to the very small $(\delta p/p )^2$, say $10^{-14}$
as suggested by~\cite{claim}, the newly ``alienated''
neutrons will slowly transit to the bottom of the nuclear
potential. The emitted gamma rays should be distinct from  those
known from capture with ordinary neutrons. With the numbers of the
previous paragraph this transition time is about one second.
 On the other hand, ordinary neutrons and protons in a nucleus
have a spectrum of semi-relativistic velocities    in any case. So
there would be a differential evolution of their properties, and
alietopes should be formed all the time. This seems to speak
against the velocity-dependent ageing hypothesis.
