1) 
evolution. Processes that imply such an
evolution affect the 
--decay time distribution.
Let 
be the rate of incoherent evolution of 
\
into 
. In the experimental setup of Sect. 2,
a fraction 
of incoherent 
would
be present all the time alongside with the 
mesons,
in equilibrium, i.e. with as many 
being formed and decaying
per unit of time.
Each one of these 
would decay into 
\
at a rate equal to 
instead of 
for 
.
Thus the coefficient 
of 
in Eq. (4)
would be increased, without 
and 
being appreciably changed.
Thus 
of Eq. (5) is not zero anymore, and one can deduce
The test of Ref. [2] yields
Note that 
is equivalent to
the parameter 
of Refs. [9] and [10]
in the context of their theory.
In the test of Sect. 3.2 that relies on the 
--decay distribution,
the incoherent 
process would act on the 
of the 
and 
systems and produce 
states after some time. As an
average in the sample of events
can be derived from 
by the same relation as Eq. (37) for 
. At Da
ne , we can hope to get
an upper limit of the order of 1/10 ms, i.e. 10
GeV.
2) 
evolution. Such process would produce 
events
in the test of Sect. 3.3.
Suppose that the uncertainty about the background in the test of Sect. 3.3
is, let us say, 100 times the contribution of the 
events,
i.e. 10
, then one could still detect
values of 
as low as 1/100 
s or 10
GeV.
3) Evolution 
--
into 
. This
evolution can be expressed also as
It will produce states where both kaons can decay into 
or both
into 
at the same time. Let us call 
the rate of this process. For the tests of Sect. 3.2 involving
or 
,
Using the estimate of Eq. (29), we could explore values of
lower than 1/0.1 ms,
i.e. 10
GeV.
If a violation of quantum mechanics is ever revealed by one
of the tests above, comparing the amount of
violation found in each test will bring information about the
decoherence mechanism responsible for the violation.
Also questions will be raised about the background
due to 
and 
events produced by 
--decay
into 
, [11].
However, the effect of this background can be
distinguished from the decoherence effects described
in this section by dividing
the sample of events into those where kaons decay near the intersection point
and those where they decay far from it.
In the test where the two kaons decay via the
mode, the 
background
populates the bin 
at z = 0 with more events when 
is small than when 
is large,
actually like 
.
On the contrary, the decoherence mechanisms take time to accumulate
events for z = 0; thus 
at z = 0
grows as a function of 
.
