In a message dated 11/11/2005 9:01:31 PM Eastern Standard Time,
stmiller@GOETHEANSTUDIES.ORG writes:
Is it true that we can think of the vacuum energy as giving rise to _any_
particle recognized by the standard model, including the force carrier
bosons such as the photon and gluon? What is the relationship between the
force carrier particles and the vacuum energy? I guess my question has to
do with how to think about _energy_... is it right to think that energy can
take the 'form' of particles; particles with mass like quarks, or particles
without mass like photons and gluons? And that it is the energy (or the
uncertainty of it!) that is primary, and what we call particles (everything
listed on the standard model) are more like particular forms of 'condensed'
or 'constrained' energy? And that in this sense of the primacy of energy,
we can imagine that the most fundamental 'thing' in the universe is actually
the quantum of action, energy x time, which follows the uncertainty relation
energy x time > h/2pi? In other words, is it possible to think of the
quantum of action as primary, and all manifest particles, including photons
and gluons, as expressions of this relation?
=======
Yes, this is true, and it is also a source a big problem in Physics, the
vacuum energy problem. In QT as far as we know all fields are quantized. ( Maybe
not gravity). This means the energy content of a given volume is
proportional to the number of quanta present in that volume. These quanta are what we
call particles. Since we can model Quantum fields as harmonic oscillators (like
an oscillation of a spring) We can write the energy equation of the field
as
E=P^2//2*m +(1/2)*m*w^2*x
Where P is the momentum, m is the mass and w is the angular velocity (
2*pi*f ), where f is the frequency)
Selecting units that set hbar=c=1 for convenience we take d/dx across the
harmonic oscillator equation and set dE/dx to zero to give us a minimum energy.
Then we solve for x we get
x=sqrt[1/(2*m*w)]
Since the uncertainty principle is
( m=E) delta(m)*delta(x)=> 1/2 we get at the limit
E(0)= w/2
So the energy eigenvalue is
E= [N+(1/2)]*w
This means that in empty space absent any particles at all we have an energy
contribution throughout the range of frequencies for each and every field.
Therefore we must integrate over the range of frequencies to get a vacuum
energy density which is
<rho>= N/4^pi^2 INTEGRAL { 0 to infinity } w*k^2dk = infinity
Where k is the wave vector ( 2*pi*P) and N is the degrees of freedom for the
fields.
We might actually expect a cut off, probably at the Planck scale so we get
<rho>= N/4^pi^2 INTEGRAL { 0 to K_c } w*k^2dk = 1E115 Gev/cm^3
This is a ridiculous result. Since the cosmological constant (Demonstrated
by Weinberg) is proportional to vacuum energy density
Lamda= Kappa*<rho>
were the vacuum energy this large the Universe would have blown itself
apart by now. This is the vacuum energy problem.
Note this vacuum energy is irrelevant until you try to incorporate gravity
into the mix. For all the other fields you just subtract out this energy by
what is called normal ordering and there is no problem. However, last time we
checked gravity does exist so this problem needs a solution.
This is a problem that has been of interest to me. One solution is to
incorporate the "real" negative energy solutions as a component of vacuum energy
which might give a scale invariant zero sum. Normally Super symmetry is
invoked to "solve" this problem (Fermions contribute negative energy to the vacuum
and SUSY proposes a Fermion Boson Symmetry)
but SUSY is badly broken at normal energy scales so really doesn't solve
the problem. I have been working with Bob Klauber on this. I actually proposed
these negative energy states as mathematical "place holders" to provide a
particle physics description of Vic Stenger's Biverse proposal and but I missed
the vacuum energy consequences in my original proposal. Dr Klauber has both
these considerations in the paper linked below. Subsequently Moffat, Kaplan
and Sundrum have also proposed these negative energy states as a solution to
the vacuum energy problem. See pre prints linked below.