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Re: [Phys-l] A New Way To Understand Gravity?


In a message dated 7/12/2007 12:49:01 P.M. Eastern Daylight Time,
betwys1@sbcglobal.net writes:

At 08:52 PM 7/11/2007, Bob, you wrote:
...Einstein.... , gravity is the
curvature of space caused by the presence of matter;

...Sakharov ...
...change in the energy density
of the vacuum [is] due to the curvature of space.
...
Bob Zannelli


This sounds like the reciprocity argument regarding force
and acceleration in Newtonian terms.

Brian I don't follow you point here
..
Bob Zannelli

I was recalling that here, people have discussed the priority of
Newton's force as causing acceleration, while others say
force and acceleration are co equal.

You mention that Einstein asserts mass causes space curvature,
while Sakharov asserts that spatial curvature causes an
energy density delta.

This seems to me like a comparable effort to assign primacy
to one term or other of some equation.


Brian Whatcott Altus OK Eureka!







Yes Sakharov proposes that gravity is not a "fundamental" force in the sense
that the EM, Strong or weak forces are. Rather what we call gravity is a
shift in the ZPE density. I am not sure how one can define what is primary,
strictly speaking. All we can say is that they relate.

What caught my interest on this is that I was surprised to learn that back
in 1967 Sakharov seems to be proposing the existence of a "ghost sector" in
the ZPE which effectively has an opposite coupling to the curvature of space
from the "ordinary" virtual ZPE states predicted by QFT in the Harmonic
Hamiltonian formalism. Of course this the troubling ZPE which based on QFT
generates a huge vacuum energy density. We deal with this by the technique of normal
ordering, it generates no QFT issues. However, as Weinberg , Zeldovitch and
others have demonstrated you can't ignore the gravitational effect of this
energy density which acts as a huge cosmological constant. The problem then
becomes why is the CC zero or perhaps near zero.

One solution proposed by Klauber, Moffat, Sundrum, t Hooft and others is to
recover the "unphysical" solutions of the relativistic equations and
postulate a "ghost" sector which cancels the ZPE of the "ordinary" virtual states. Of
course these are the true negative energy states which Pauli demonstrated
can't exist as physical particles. These states are resurrected however by
postulating that they do not couple via the fundamental forces. Of course the
"ordinary" and ghost sector contribute opposite signed vacuum energy density.


What Sakarov proposes is that this cancellation occurs only in flat space.
What we call a gravitational field is when this cancellation isn't perfect.
Of course in GR a non zero vacuum energy density generates space curvature and
relates to the cc.




Below is one of the posts I did a while back where I attempted to flesh
this out. This idea also has a relation to what has been called the Biverse by
Dr Vic Stenger , another proposal which shows up in another 1967 Sakharov's
paper where he defines the condition needed to create the matter-antimatter
imbalance we observe. This idea has also been proposed by Stenger, Linde and
others.








INDUCED GRAVITY WITH SAKHAROV QUOTES
I have made several posts on the possible connection between A.D. Sakarov's
1967 "Induced Gravity" proposal (" Vacuum Quantum Fluctuations in Curved
Space and the Theory of Gravitation.") and the new proposal by several physicists
on the existence of a negative energy "ghost" sector which is hoped will
solve the Zero Point Energy problem, the non existence of a huge vacuum energy
density which would generate a huge cosmological constant, so large in fact
the structure we see in our Universe would be totally impossible.
I think some direct quotes from Sakarov's original 1967 paper may be
helpful.
Sakharov writes
“Here we consider the hypothesis which identifies the action
(Einstein-Hilbert action) with the change in the action of quantum fluctuations of the
vacuum if space is curved. Thus we consider the metrical elasticity of space as a
sort of level displacement effect.) (See E.M Lifshitz zH ekap .Teor. Fiz.29,
94 (1954) [Sov. Phys-JETP2, 73 (19540]
“In present-day quantum field theory it is assumed that the energy momentum
tensor of the quantum fluctuations of the vacuum T^i_k(0) and the
corresponding action S(0) , formally proportional to a divergent integral of the fourth
power over the momenta of the virtual particles of the form - Integral k^2
dk - are actually equal to zero."
“Recently Ya B. Zel'dovitch [ ZhETF pis.Red. 6 922 (1967) [JETP Lett.6 245
(1976)] suggested that gravitational interactions could lead to a "small"
disturbance of this equilibrium and thus to a finite value of Einstein's
cosmological constant, in agreement with the recent interpretation of the
astrophysical data. Here we are interested in dependence of the action of the quantum
fluctuations on the curvature of space."
End Quote
Sakharov then goes to derive the gravitational constant from the second term
of a Lagrange power series function of curvature terms.
The quantum fluctuations in question are the result of applying the
uncertainty principle to the harmonic Hamiltonian which results in
H= w*[a^dag*a + (1/2)] (for boson fields)
Note I will ignore the fermion states because mass spitting make the
predominate contribution due to virtual boson particles, especially the
electromagnetic field.
Giving us a energy eigenvalue of
E= (N+ (1/2*)*hbar*w
So given the vacuum state [0> we have
E (w) = hbar*w/2
So we have to integrate over the whole energy spectrum of the virtual
particles
< rho> = (1/4*pi^2)*Integral { 0 to k_c} w*k^2 dk
Which is the integral Sakharov mentions in his paper.
This gives a huge divergent vacuum energy density. Even at the expected cut
off, the Planck scale, the vacuum energy density prediction is off from the
value constrained by observation by a factor of 1E120.
The solution to this dilemma is to invoke a "ghost" sector for virtual
states. In this Ghost sector we have
a_gh= -i*a^dag a_gh^dag= -i*a
Given us the energy eigen value
E= -(N+1/2)*hbar*w
So that for the vacuum state [0> we have
E (w) = -hbar*w/2
Which gives us < rho> =- (1/4*pi^2)*Integral {0 to k_c} w*k^2 dk
Thereby giving us an overall zero vev for the vacuum.
However, based on the Zel'dovitch-Sakharov proposal on the effect of
gravitational interactions on the "equilibrium" of vacuum state we can postulate
that this proposed balance between the normal particle sector and the "ghost"
sector holds only in a space time metric with zero curvature. In GR we have
the relationship
R_mu,nu-(1/2)*R*g_mu,nu= -( 8*pi*G/c^4)*<rho>*g_mu,nu
So given a positive vacuum energy density we have negative curvature and
given a negative energy density we have positive curvature.
This suggests that a condensed physics analog might be appropriate in
modeling the vacuum state. And since we can equate the vacuum energy state with
space time curvature , we can equate the gravitational field with the energy
density of the vacuum relative to an observer in a gravitational field.
We can view a space time with positive curvature as related to a local
vacuum state which is "depleted" in the action density of the normal virtual
states or equivalently an increase of the action density of the virtual particles
in the ghost sector.
Likewise we can view negative curvature as related to a local vacuum state
which is "depleted" in the action density of the Ghost sector virtual states
or equivalently an increase of the action density of the virtual particles in
the normal sector.
But is there any mechanism which can relate to this "depletion?" I think
here we get a hint from the Davies-Hawking-Unruh effect. Based on the
equivalence principle gravity is an acceleration field. Therefore we see that
T= (hbar/2*pi*c)*dv/dt
In any non inertial frame virtual particles are "promoted" into real
particles. In effect acceleration "measures" the vacuum state. But does such a
process really deplete the appropriate virtual states of the vacuum to generate
the curvature of space time predicted by general relativity. Perhaps a look
at Black holes and the Hawking process in light of this proposal may be
helpful.
We need to invent a notation to make the explanation clearer.
We can define the four possible matter states, two normal, two in the ghost
sector, using the ket notation.
We use the SGN function which is
x>0 SGN[x] = +1
x<0 SGN[x] = -1
x=0 SGN[x] =0
We have the four matter states defined as
Psi= [SGN [E] SGN[t] >
So that
NORMAL SECTOR
Matter (Positon)
psi_m= [+ + >
Anti matter (positon)
psi_am = [- - >
GHOST SECTOR
Negative matter (Negaton)
psi_nm = [- + >
Negative anti matter (Negaton)
psi_nam = [+ - >
The Zero point energy fluctuation can be positive or negative in this
proposal.
Positive fluctuation can be modeled as
[0 0 > = [+ + > + [- - >
And a Negative Fluctuation can be modeled as
[0 0 > = [+ - > + [- + >
Now we introduce a black hole horizon and look at the Hawking process. We
can model this as a virtual pair being created and one member of the pair
crossing the horizon. Now negaton particles can not cross the horizon toward the
singularity because they anti gravitate. So we can that only positive
fluctuation can create the Hawking radiation.
[+ + > + [- - >
So we end up with (as one of two possibilities)
[+ +> to infinity and [- - > crossing the horizon.
Well this represents a depletion of positon virtual states. In fact the
Hawking process does in fact require that the vacuum state just outside the
horizon violate the weak energy condition relative to a particle being emitted
from a black hole event horizon. Therefore we have;
Rho<0
Can we model this for negative curvature? We can use a thought experiment
with a negative mass black hole which would generate an anti-Horizon. Of course
such a black hole does not exist in our Universe.
Here we can say that positon particles can not cross the horizon toward the
singularity because they gravitate. So we see that only negative fluctuation
can create the anti- Hawking radiation. Given
[+ - > + [+ - >
We end up with (as one of two possibilities.)
[+ -> to infinity and [+ - > crossing the horizon.
This represents a depletion of negaton virtual states.
So we would get
Rho>0
But of course we can never have real negative energy particles. This is of
course true but it must be remembered all measurement events are
manifestations of the decoherence process whose functional has a positivity requirement.
Therefore while the negaton is a negative energy particle in its virtual state
it can only be measured as positive energy particle. Of course this point
must be dealt with in much greater rigor than this hand waving explanation.
Hopefully a better understanding of the Decoherence process might allow this
point to be better formulated.
I will close this with another quote from Sakharov's paper.
“Consideration of the density of the vacuum Lagrange function in a simplified
model of the theory for non interacting free fields with particles M approx
k (0) shows that for fixed ratios of the masses of real particles and "ghost"
particles (i.e. hypothetical particles which give an opposite contribution
to that of real particles to the R dependent action) a finite change of action
arises that is proportional to m^2R which we identify with R/G. Thus the
magnitude of the gravitational interaction is determined by the masses and
equations of motion of free particles, and also, probably, by the momentum
cut-off"
End quote
It occurs to me that all the ideas which have intrigued me such as the
Biverse and the application of negative energy state in the ZPE formulation was
just unknowingly following in the foot steps of A.D Sakharov.
Bob Zannelli














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