The really unique tests of quantum mechanics at Da
ne are
tests with quantum states made of two kaons.
In 
--collisions of this kind of energy, only objects odd
under charge conjugation are formed. The two-neutral-kaon system
created via 
production and two-body decay in a given direction is
in a pure quantum state. Its state vector can be expressed as
In the terms 
, 
, 
, and 
, the first symbol
refers to the state of the particle emitted on the left and the second
symbol to the particle on the right. The sign 
is used in
Eq. (8) instead of the sign = because of a slight inaccuracy in the
normalization factor.
As stated above, kaons living long enough to be reduced
to their 
component
are pure states and 
--decay states are equivalent to
pure 
S--wave states. If we accept the 
rule,
each of the semileptonic decay states 
\
and 
can also be considered as a pure state in the context of
this paper. As to multiple-particle states where the kaon
on the left has decayed into a pure state 
and the kaon on the right
into a pure state 
, they are pure states themselves.
All processes leading from
the initial 
--meson to any one of these pure
multiparticle final states 
interfere between each other.
In particular, consider the possibility of having the same decay state f,
for instance 
, or 
, or 
, as the final decay product
on the left as well as on the right.
This may happen via two processes,
1) a 
emitted to the left and a 
to the right; or
2) a 
to the left and a 
to the right;
and, in either case, both the 
and the 
decaying into the
same state f. These two processes interfere between one another.
Let 
and 
be the branching ratios of 
and 
,
respectively, into the decay state f .
From Eq. (8), one gets the probability for the kaon
on the left to decay into f at the proper time 
and
the one on the right to decay into f at proper time 
,
per unit of 
and unit of 
:
The third term in the largest bracket of Eq. (9)
is the interference term.
For 
, that term is negative and large enough to
make 
.
However, if, for any reason, the interference term is reduced by
a factor 
, the rate for 
becomes non-zero.
These conditions are particularly favorable for a test of quantum mechanics
because, then, the test for 
is a null experiment.
