In a message dated 10/12/2006 10:09:00 AM Eastern Standard Time,
Spinoza321@aol.com writes:
In the paper "Mechanism for Vanishing Zero Point Energy" by Bob Klauber
(available in E Print archive) he points out the all the relativistic
equations,
Klein Gordon, Dirac and Proca have solutions which he calls supplemental in
addition to the Traditional solutions. For example in the Dirac equation
there really has eight eigenspinor solutions instead of just four. Pauli
demonstrated that these addition solutions are unphysical, they are the
negative
energy states which are a disaster in QFT.
Bruce Kellet talks about these solutions in his Paper "The Asymmetry of
Radiation," ( I will make this paper available to anyone on request) As I
have
mentioned before, I highly recommend this paper for a clear description of
the arrow of time problem with regard to radiation.
Everyone agrees that these supplemental solutions are unphysical, they
will never be seen as real particles. However, Klauber has proposed that
these
supplemental states can "exist" as virtual particles which can be used to
solve the ZPE problem. Similar proposals have now be made by Moffat,
Randel,
Sundrum and T Hooft. These supplemental states also directly relate to the
Biverse proposal and Linde uses these negative energy states to zero out
all of
the vacuum energy contributions in a paper available in the archive.
But the purpose of this post isn't to argue these points one way or the
other. Rather I will show by very simple mathematics that what really
separates the physical from the unphysical states are the sign of the
invariant mass
term. I invite critical comments if this point is of interest to anyone.
Here's is the formulation in complete form.
c=1
E=gamma*m
p=gamma*m*v
gamma= E/m
tau=t/gamma
tau/t=m/E
v= E/p
Traditional States ( Physical States)
MATTER w(+) & k(+) (Positive Energy into Future )
tau(+)/t= m(+)/E(+)
v(+)=E(+)/P(+)
gamma(+) = E(+)/m(+)
E(+)= gamma(+)*m(+)
p(+) =gamma(+)*m(+)*v(+)
ANTI MATTER w(-) k(-) ( Negative energy into past)
tau(-)/t= m(+)/E(-)
v(+)=E(-)/P(-)
gamma(-) = E(-)/m(+)
E(-)= gamma(-)*m(+)
p(-) =gamma(-)*m(+)*v(+)
SUPPLEMENTAL STATES ( Unphysical States)
NEGATIVE MATTER w(-) k(+) (Negative Energy into future)
tau(+)/t= m(-)/E(-)
v(-)=E(-)/P(+)
gamma(+) = E(-)/m(-)
E(-)= gamma(+)*m(-)
p(+) =gamma(+)*m(-)*v(-)
NEGATIVE ANTI MATTER w(+) k(-) (Postive energy into past)
tau(-)/t= m(-)/E(+)
v(-)=E(+)/P(-)
gamma(-) = E(+)/m(-)
E(+)= gamma(-)*m(-)
p(-) =gamma(-)*m(-)*v(-)
It all holds together nicely. Not Profound but interesting.