Subject: An alternative view of ZPF
Dear Dr. Haisch:
Thank you very much for sending us your latest paper on ZPF.
I was also somewhat amazed to see the latest broadcast by Bob Park, where he
argues that advocates of ZPF should be treated, in effect, as lunatics and
outcasts, without the same rights to scientific treatment that the
scientific method is supposed to offer to all serious points of view.
Jack Sarfatti: I have not seen what Park has written. He is over-reacting to
the fact that there is so much hype about zero point energy breakthroughs in
the New Age Flake Press like Nick Cook's book "Hunt For The Zero Point",
Brian O Leary's book and others. Also Bernie and Hal have not helped this
media situation. Joe Firmage, the brief Dot.Com 20's something millionaire,
caused a lot of damage by including their work in his public talks some
heard by important physicists like Brian Greene who then no doubt went on to
tell all his colleagues about Joe being a crackpot. Then you have political
groups like UFO Disclosure and Ban US Space Weapons citing Bernie and Hal as
backing up their phony claims of secret US Black Ops zero point energy
anti-gravity weapons systems, oil energy alternatives and other nutty
allegations. This, I suspect, is why Parks is on the war path against Hal
Paul: At some level, all you are saying is that the
"1/2 w**w" terms that we usually throw out from the Hamiltonians of quantum
field theory (QFT) should not be
totally thrown out, because they may have physical implications, like the
Casimir effect. Given that this view
is endorsed very clearly but briefly in Weinberg's text, clearly and at
greater length in the equally authoritative
text of Zinn-Justin, and assumed in virtually of the Hawkings and Forward
stuff, it is incredible that anyone should
brand it as heresy.
Jack: I doubt that this is what Parks was alluding to.
Paul: Yet, at the same time, as a confessed heretic myself, I would like to
suggest an alternative to the ZPF idea
which I hope someone will consider seriously.
The key idea is as follows. First, we assume (for now) that the universe is
governed by the
basic "Schrodinger equation"
psi-dot = i H psi.
In the traditional texts on QFT, the operator H is derived as follows.
First we work out the Hamiltonian functional
H for some classical Lagrangian field theory. ( It should be script-H, but
this is ASCII.) And then,
for each reference to a field phi(i,x,t), we replace that reference by the
"corresponding" operator field.
That gives us the H of QFT. It also gives us zero point terms. And then, in
the usual texts, it says something like "we can
just assume that these infinite-energy terms actually equal zero, because
they couldn't affect anything anyway."
Now: here is my proposal: IN THIS quantization step, I propose that we
should still DEFINE the quantum Hamiltonian
as the result of the usual substitution, BUT WITH the classical
"multiplication" operator replaced by the NORMAL PRODUCT
in all cases. In that case, the quantum mechanical Hamiltonian DOES NOT
HAVE zero point terms at all.
This becomes part of the DEFINITION of the theory, of the quantization
Jack: No this is wrong. Indeed, the evidence from astronomy is that the
acceleration of the universe and the dark matter are zero point vacuum
energy contributions to the variable cosmological /\ field. The basic way
this works is in Peacock's "Cosmological Physics" and Milonni's book "The
Quantum Vacuum". Then there is spontaneous emission, the Lamb shift et-al.
There are many advantages of this formulation, some of which I discovered
from work along a totally different line.
This formulation is what motivated me to re-examine everything I could find
on the Casimir effect, on the suppression
of stimulated emission in certain classes of lasers, and so on -- all of
which convinces me that this is a viable model
consistent with everything we know. What we lose in terms of short-term
hopes for technology we may make up for in other sectors
of new possibilities.
Among the pieces of logic here....
in the general case, the ordinary quantization map is not even
well-defined. Sequences of products in the classical
Hamiltonian can be written in any order, yet the field operators do not
always commute. But the normal-product
quantization map is well-defined.
And then... ONE PART of my paper quant-ph 0202138... it turns out that the
normal form Hamiltonian really corresponds
'to the Hamiltonian of the original classical field theory, in a way that
the ordinary one does not.
Let me be more specific here.
The statistical moments of an unknown classical field phi(i,x) at any time
are usually defined as:
un = < phi(i1,x1)*phi(i2,x2)*...*phi(in,xn)>
At first glance, the collection of such moments would appear to form a
vector in the ordinary Fock-Hilbert
space, the same one that a bosonic wave function would be defined over. But
it does not: it does not have
a finite norm, even for fields phi which do. However, by scaling the
moments to have a unit norm
in Fock-Hilbert space, and appending the conjugate variables, we do arrive
at a matrix rho over Fock-Hilbert space
which represents the statistical moments of the state of a classical field
-- the "classical density matrix" as defined
in quant-ph 0202138.
It then turns out that tr(rho H) yields the expected value of the energy of
that classical field, exactly, **IF** H is
the normal form Hamiltonian. This exact equivalence between a classical and
a quantum field theory is of some interest.
I do have very detailed (if tedious) proof typed up for every single
equation in quant-ph 0202138. Unfortunately,
I have found some holes in the VERBAL analysis of the implications; more
precisely, the Liouville equation for
the dynamics of the field operators is NOT enough by itself to deduce all
the rest of QFT, even though Weinberg's arguments
appear to suggest that it is. I have some ideas about how to deal with
that, but competing pressures here at NSF
limit the time I have to study such extensions. The normal product part,
however, is quite clear and quite rigorous.
P.S. quant-ph 0202138 also suggests an alternative way to replace the
present Higgs model, so as to eliminate
the need for renormalization. This would only go through with the normal