Monday, April 09, 2007

Of course the model below is only a toy model illustrating a set ideas organized in an unfamiliar way in an attempt to shed some light on the greatest mystery in physics today

What is our universe mostly made of?

Jack Sarfatti ( wrote:
Decoding The Cipher of Genesis

Looking at elementary cavity quantum field theory for a scalar field U(x,t) in 1+1 spacetime, e.g. string standing wave oscillations, the mass shell condition f = (signal speed)k for zero dispersion and zero rest mass is enforced by boundary conditions e.g. U(0,t) = U(L,t) so that

f(l) = l(signal speed)/2L

where l is the mode index that in this simple case is an integer 1 to infinity.

group speed = signal speed = phase speed

in this non-dispersive toy model.

The resulting Fock occupation number states |n) are n identical real on shell quanta each of frequency f(l) in the lth mode of wave length 2L/l with l = 1 the fundamental, l =2 the first harmonic and so on. The Fock space vacuum of a given mode with n = 0 has an effective random noise occupation number of 1/2.

In contrast to Fock states that are orthogonal inside a single mode (the modes are, in addition, mutually orthogonal)

(n|n') = 0 when n =/= n'

The macroquantum ODLRO coherent Glauber states |z) are coherent superpositions of different numbers of "real" quanta they are not orthogonal for a given l mode, i.e.

(z|z') =/= 0 ODLRO states when z =/= z'

z is a complex number

z = (n)^1/2e^itheta

theta is the coherent phase

(n) is the mean occupation number

Uncertainty principle

delta(n)delta(theta) ) 1/2

z is a displaced Gaussian in the complex z-plane

|z) = e^(z*a - za*)|0)

|0) is the Fock space vacuum for the single lth standing wave mode of the 1D cavity.

aa* - a*a = 1

a|0) = 0

(0|a* = 0

The single mode Hamiltonian is global over the entire cavity space

H(l) = hf(l)[a*(l)a(l) + 1/2]

I will drop the l for simplicity, understood only a single standing wave mode of sharp wavelength and a definite frequency.

(0|H|0) = hf/2

is the random zero point energy ZPE of that single mode.

This zero point energy in the Fock vacuum |0) directly antigravitates repulsively like an isotropic fluid with w = - 1 in the 3D case - not the present 1D model.

You can think of microquantum |0) as a toy model for the unstable false pre-inflation random incoherent vacuum whose collapse to a more stable less random more coherent macroquantum Glauber state ODLRO "superfluid" vacuum |z).

OK so here is how to do the ODLRO "superfluid" for this single mode.

a = A + @

A is the ODLRO c-number condensate

@ are the random zero point quanta in the coherent vacuum at absolute zero temperature where there are no on-shell elementary excitations "normal fluid" excited states above this Higgs field vacuum where theta is a Goldstone phase.

H(ODLRO) = hf(A* + @*)(A + @) + hf/2

The Glauber states |z) are defined relative to the @ and @* second quantized single-mode destruction and creation operators NOT the original a & a*.

a & a* are the pre-inflation false unstable vacuum operators

@ & @* are the post-inflation dark energy-dark matter metastable vacuum ZPE operators at absolute zero temperature prior to the hot big bang creating ordinary matter and radiation that is only 4% of all the stuff of our accelerating expanding pocket universe in the cosmic landscape of the megaverse of parallel universes including the parallel Virgin Earth's that are part of our Manifest Destiny Matrix - the space migration now professed by Stephen Hawking.

The energy of our false incoherent Fock vacuum without any ODLRO macroquantum condensate is

(0|H|0) = (0|(hf + 1/2)a*a|0) = hf/2

The energy of our more stable coherent vacuum condensate is

(z|H(ODLRO)|z) = hf(|A|^2 + A*z + Az* + |z|^2 + 1/2)

Note if |A| = 0 i.e. no ODLRO

(z|H|z) = ((n) + 1/2)hf ) (0|H|0)

The energy difference of the vacuum phase transition in this single-mode 1D toy model is

(z|H(ODLRO)|z) - (0|H|0) = hf(|A|^2 + A*z + Az* + |z|^2) < 0 stability

|A|^2 = vacuum condensate density

is it real or virtual quanta? (Larry Krauss in "Quintessence")

What does that distinction even mean here?

I opt for virtual since we are at absolute zero.

In superfluid helium at absolute zero the condensate density is 10%, the zero point density is 90% and the total superfluid density is the sum 100% with zero % normal fluid real particles at finite temperature - in thermal equilibrium approximation of course.

|z|^2 = zero point dark energy/matter density

The cross terms are the flow of virtual random quanta into and out of the coherent vacuum condensate reservoir out of which the curved fabric of spacetime emerges as I showed elsewhere.

The energy density per mode released in this first order vacuum phase transition making the hot Big Bang that creates the 4% ordinary matter and radiation we are made out of is determined by the coherent Goldstone phase lag constraint

Vacuum Condensate Density + Dark Energy ZPF Density

+ 2(Vacuum Condensate Density)(Dark Energy ZPF Density)^1/2cos(Goldstone Phase Lag) < 0

Phase lag is between the vacuum condensate phase and the ZPE dark energy phase in this 3 fluid (not 2-fluid macroquantum cosmology toy model with advanced signal retrocausality - discussed elsewhere (pun intended).

These quantum energy densities can go negative.

Either the vacuum condensate energy density or the ZPF energy density can be negative.
Let their ratio be x. The stability inequality is

x + 1/x < 1

therefore x < 0.

positive ZPF energy density is repulsive dark energy

negative ZPF energy density is attractive dark matter

of course the model below is only a toy model illustrating a set ideas organized in an unfamiliar way in an attempt to shed some light on the greatest mystery in physics today

What is our universe mostly made of?

Jack Sarfatti ( wrote:
Sidney Coleman's 1973 Erice Lectures on Hidden Secret Symmetries i.e. spontaneous broken symmetry of ground state comes closest. But Kraus's formulation of the problem may be spurious.

If we have a generally locally variable Higgs field of n real components Psi(x,t) its Fourier integral (assume globally flat spacetime for now) will have components for all frequencies and all wave vectors - hence a mass shell condition makes no sense.

Coleman defines the vacuum condensate for a renormalizable quartic (Mexican Hat) spin 0 scalar quantum field in terms of the connected generating functional W(J) where

e^iW(J) = (0+|0-)

vacuum to vacuum Feynman amplitude

The classical ODLRO vacuum condensate field Psi(x,t) is the functional derivative of W with respect to external source current density J(x)

The effective action is a functional Legendre transform of the generating functional by the global integral of J(x) multiplies by the ODLRO condensate field.

The effective action is also a Taylor series expansion of all nth order IPI Green's functions of the scalar field with nth order product of the ODLRO order parameters. Now I think those IPI Greens functions are all virtual quanta exchanges because "no propagators on the external lines" but I am not sure.

One then gets an effective potential V of the ODLRO vacuum condensate order parameter.

This only scratches the surface of course. Not a solution.

Jack Sarfatti ( wrote:
The problem is not trivial. Appeal to BCS Green's function not good because the condensate there, and in superfluid helium, is on shell real particles in a ground state.

In the case of the actual Higgs field of our universe from inflation out of which curved spacetime emerges, i.e. the tetrad and spin connection 1-forms from the Goldstone phases of the ODLRO coherent vacuum - the issue is are there pole contributions to the vacuum in the Green's functions for elementary excitations of the coherent vacuum, or are the pole terms only in the elementary excitations of the pre-inflation false vacuum prior to the Cosmic Trigger advanced signal from the future deSitter horizon of the emergent pocket universe on the Landscape? The advanced signal lowers the entropy of the early universe explaining how the Arrow of Time of the Second Law of Thermo is "parallel" to the now accelerating expansion of 3D space.

Larry Krauss writes in his book "Quintessence":

"phase transitions in the 'vacuum' (or ground state) of nature can occur. In such cases a finite density of real particles might 'condense' into the new vacuum state." p. 41

If the macro-quantum ODLRO part(s) is from a pole(s) in the appropriate Green's function(s) then Kraus is correct, i.e. if there is a mass shell constraint p^upu = m^2 for the quanta inside the effective BEC(s). There is no microscopic theory of the inflation Higgs field(s) as yet.

For example, in the Glauber state |z) of quantum optics where

a|z) = z|z)

z = (n)^1/2e^i(coherent phase)

f = ck for transverse radiation real photons on mass shell (here mass shell = light cone)

is true physically.

However if one uses a wavelet mode basis this need not be true at all.

A finite spatial wave packet has many k for same frequency f like a virtual photon. This is physically important in a cavity. Of course, such a wavepacket may also have a frequency spread where f = ck.

In the quantum oscillator problem one only uses f and then ad-hoc imposes f = ck in the case of far field transverse photons. However, one can imagine coherent states of virtual photons off mass shell including longitudinal polarization in which a given f has all possible k.

That is, the second-quantized operators a & a* where aa* - a*a = 1 do not refer to plane waves in infinite space but are wave packets inside a cavity.

Note also that the classical static Coulomb potential

V = +- e^2/r

consists of virtual longitudinal photons in a macroquantum coherent f = 0 (DC) state with all possible k momenta i.e.

Vk ~ e^2/k^2

1/k^2 is the almost photon propagator Green's function i.e.

e (1/k^2)e

is essentially a Feynman diagram with charges e at each vertex (dot) and a wiggley virtual photon line connecting the two dots.

To add advanced and retarded boundary conditions

1/(k^2 +- iepsilon)

Jack Sarfatti ( wrote:

Larry Krauss in his 2000 book "Quintessence" says the vacuum condensate is a large number of Bose-Einstein condensed real on shell particles in the same single-particle state. I picture them as virtual off-shell. Who is correct? Must look at Gorkov theory of BCS Green's functions with ODLRO to see what is what here. Real particles are poles in complex energy plane of Green's functions. Pole + off pole parts at T = 0 is 100% L-G superfluid density. Off pole part = locally incoherent nonlocally coherent EPR entangled ZPF if pole part is the ODLRO condensate. I am checking into this.

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