Friday, July 21, 2006

Star Gate
Commentaries on The New Physics
for the 21st Century
Jack Sarfatti, Ph.D.
Theoretical Physics
University of California

Everyone thought that gravity universally attracts everything to each other until very recently when astronomers discovered dark energy at the beginning of the 21st Century. The dark energy is a very weak universally repelling cosmic field on large scales that causes the rate of expansion of three-dimensional space to speed up, to accelerate, rather than to slow down, to decelerate, as everyone mistakenly thought. It is important to realize that both gravity and dark energy are not ordinary forces acting on matter but are “geometrodynamic” properties of the intrinsic fabric of space itself. This delicate distinction will be explained in more detail below.
The discovery of the cosmic dark energy is like the discovery of the shape of the blackbody radiation spectrum at the beginning of the 20th Century. The fact that the radiated energy of the blackbody radiation decreased with increasing frequency caused Max Planck to begin to invent quantum theory. The classical physics of Maxwell’s electromagnetic field theory broke down for blackbody radiation because it wrongly predicted an absurd infinity. The very cold redshifted Cosmic Black Body Radiation (CMBR) filling the three-dimensional space of our expanding accelerating universe today is important evidence that there was a very hot Big Bang at the creation of our local pocket universe in the Megaverse Cosmic Landscape of parallel pocket universes suggested by the theory of eternal chaotic inflation describing the cold moment before the hot Big Bang - first Ice then Fire! How come the pre-Big Bang pocket universe was cold with small entropy? That’s a happy coincidence needed to understand the “Arrow of Time” of the irreversible aging leading to our mortal deaths of the Second Law of Thermodynamics. Why do we get older as our pocket universe’s 3D space expands? The answer seems to be that advanced signals from the far future reach back to the initial inflationary quantum vacuum phase transition to lower its thermodynamic entropy. More on this later in the book.

Gravity is important on both the shortest and the longest scales of space-time. It is important on the shortest scales because of the weak equivalence principle that demands that all forms of energy, both real and virtual in the sense of quantum theory, curve spacetime. The smallest scales have the largest energy fluctuations causing the formation of tiny virtual blackholes that can even sprout baby pocket universes out of ours.
Gravity is different from electromagnetism, the weak radioactive and the strong subnuclear forces because gravity free-fall acceleration is universal and the other forces are not. This was first understood by Galileo hundreds of years ago before Newton. All neighboring uncharged non-spinning objects (AKA “test particles”) in a vacuum fall with exactly the same acceleration. Einstein generalized Galileo’s observations to the principle of subluminal timelike geodesic motion of massive test particles in curved space-time. The slower-than-light geodesic is the straightest possible world line in four-dimensional space-time. It looks curved in three-dimensional space like the elliptic orbit of the Earth around the Sun as an example. This appears to be a “force” in the Newtonian way of thinking, but there is no gravity free-fall force in the Einsteinian way of thinking. Many people, even some physicists, have difficulty in understanding this idea properly. Each point on the timelike geodesic path is inside its local invariant light cone. The curvature of space-time corresponds to a relative tilt in the field of light cones. What we call “g-force” that you feel when an elevator starts to move, or when you stomp on the accelerator of a powerful car, or catapult off an aircraft carrier, or blast off in the Space Shuttle is actually non-geodesic motion caused by some kind of non-gravity force. In every day life the only effective non-gravity force is the electrical force that also determines the combustion of jet and rocket fuel along with the quantum Pauli exclusion principle. The Paul exclusion principle prevents identical spin ½ particles (electrons, nucleons) from occupying the same quantum state. This ensures the diversity and stability of the forms of ordinary real matter out of which we are made.

Of course, ordinary real matter is only about 4% of all the “stuff” in our pocket universe piece of the Megaverse. Universally repelling virtual positive dark zero point vacuum energy density with equal negative pressure is about 73% of the world stuff generating the local “Ricci curvature” of the fabric of spacetime. The remaining 23% is, in my opinion, universally attracting negative zero point vacuum energy with equal positive pressure. This is called “dark matter”, also a local source of Ricci curvature, although it does not consist of any real exotic particles at all in my opinion. Therefore, I predict that the Large Hadron Collider will not find any dark matter particles at all that can account for the missing 23% seen in galactic halos for example. What determines the sign of the gravity influence, universal attraction or universal repulsion is the sign of the quantum pressure not the sign of the quantum energy density because, according to Einstein’s general theory of relativity, the pressure outweighs the energy density by a factor of three at least in the case of no Casimir type effect boundaries. This factor of three comes from the equivalence principle.
“Einstein’s great idea, that gravity is curvature of spacetime, is based on the equivalence principle. … All objects are acted on by gravity and fall to the floor with the same acceleration in the Earth lab; in the rocket ship the lab floor accelerates and catches up with the [free floating] objects, so they appear to accelerate toward the floor at the same rate. From inside the lab one cannot tell from such experiments whether one is in a gravitational field or in an accelerating lab: they are equivalent. There is also a converse of this equivalence … If we let the Earth lab fall freely then objects inside will accelerate along with it and appear to float, just like in the rocket lab [out in far empty space] with the motor turned off. We can think of gravity as being transformed away in the freely falling lab. Einstein called this insight his ‘happiest thought’. … we certainly cannot think of the Earth as accelerating outward … Einstein showed that we obtain the same effect if spacetime is curved. For bodies moving slowly in a weak gravitational field such as the Earth’s, it is the warping of time that produces the effect of gravity, while the warping of space is less effective. … the Earth’s gravity is due mainly to the fact that a clock near the surface runs slightly slower than a more distant clock even though the amount of the slowing is only a few parts in 10^8.” Ronald Adler in “The New Physics for the Twenty-First Century ed. G. Fraser, Cambridge 2006

The accelerating rocket frame out in empty deep space with motor on is called “LNIF” for Local Non-Inertial Frame as compared to the geodesic LIF for Local Inertial Frame when the rocket motor is switched off and therefore the rocket center of mass is on a timelike geodesic worldline or path or history. The rocket world line with motor on is still timelike always inside its momentary light cone, but it is not geodesic. Time passes slightly slower when the rocket motor is turned on compared to when it is turned off. The geodesic is the straightest worldline in 4D curved spacetime. It is a critical point in the geometrodynamic action for the motion of a test particle in the space of possible worldliness. It is where the Feynman quantum amplitudes for each path constructively interfere with each other.

One can, of course, measure curvature by measuring the vacuum “conformal Weyl” tidal relative acceleration between pairs of neighboring objects at the second order of smallness in the sense of a Taylor series expansion of the metric field in differential calculus. The above statement of the equivalence principle is only meant to the first order of smallness in the metric field. It is the metric field that determines the physically invariant infinitesimal separations for arbitrary local choices of local coordinates. This arbitrary local choice depends on three sub-choices. Is the motion of the local rocket frame geodesic or non-geodesic? How are the spatial coordinate grids painted and how is the local clock calibrated. How these sub-choices are made is completely subjective – pure art. Do as thou wilt at that level of “representation” of the local objective structure of “classical reality” ignoring nonlocal quantum entanglements of critical degrees of freedom of distantly separated detectors. What counts here is always the relevant “total experimental arrangement” in Niels Bohr’s sense.
The locally frame invariant geodesic equation is symbolically in intuitive form
X;ds;ds = 0
where X is the location of the test particle, ds is the invariant differential (infinitesimal) proper time and ; is a covariant derivative operator we will define more carefully later on. It depends on a connection field for the transport of vector arrows parallel to itself along an arbitrary path. This is the equation for the uncharged non-rotating test particle. If the test particle has electric charge and there is an electromagnetic field we have a new non-geodesic equation
X;ds;ds = F/m
F is the electromagnetic force and m is the mass of the charge. This is simply Newton’s 2nd Law of Mechanics generalized to curved spacetime. We can also make similar equations for the rocket of mass M, but we then get an additional term ~ M;ds since the rocket is losing mass when it ejects propellant. This does not happen in weightless warp drive (WWD) where the equation of the alleged alien ET flying saucer out of hyperspace is still the geodesic equation above. The new feature is that the crew inside the saucer is able to control the shape of its momentary local timelike geodesic for their ship’s center of mass with small Weyl conformal tidal stretch-squeeze forces across the ship end-to-end. This is what “metric engineering warp and wormhole” is all about.
The measurement of vacuum Weyl conformal tidal curvature requires two neighboring neutral zero spin test particles each free-floating on timelike geodesics separated by &X. The equation of their tidal geodesic “stretch-squeeze” deviation is symbolically and intuitively of the local frame-invariant form
&X;ds;ds + CX;dsX’;ds = 0
&X = X – X’
and C is the vacuum Weyl conformal curvature tensor piece of the full Riemann-Christoffel curvature tensor whose “Ricci” part is zero in an ordinary vacuum with zero dark energy/matter.
Let the metric field be “g”. The connection field is first order ~ g ,u where ,u is the ordinary partial derivative in the u-dimension, the curvature field is second order ~ g,u,v
The Taylor series expansion of metric field g from point Po to point P is then of the form
g(P) ~ g(Po) + g(Po),u(P – Po)u + (1/2)g(Po),u,v(P – Po)u(P-Po)v + …
This is symbolically and heuristically
g(P) ~ g(Po) + (Connection at Po)(P – Po) + (Curvature at Po)(P – Po)2 + …
with the connection and the curvature fields embedded inside the first-order linear and second-order quadratic expansion corrections respectively
The condition for the geodesic LIF is like a test-particle action extremum
(Connection at Po) = 0
This is like a max or min or inflection critical point in elementary calculus for
y = f(x)
The sign of the “curvature” second derivative is whether we have a max, or min etc.
In terms of my vacuum ODLRO emergent coherent gravity model, the metric field is a symmetric bilinear product of the Cartan tetrad 1-forms e, where symbolically and intuitively, more rigorous discussion will come later in the book
g(Curved) = e(Flat)e
e = 1 + A
A has the physics of curvature and it comes from two effective coherent vacuum ODLRO Goldstone phases Theta & Phi of the inflation field where the geometrodynamic area flux density 2-form is
dA = (hG/c^3)d(Theta)/\d(Phi) = (Planck Area) d(Theta)/\d(Phi)
with point singularities in the single-valued inflation field. Therefore, the integral of dA over a surface without boundary that surrounds the singularity is quantized
Area ~ Integer (Planck Area)
That is the geometrodynamic degrees of freedom have area flux quanta. The geometrodynamic “volume” operator d^2A = 0 in this theory as in the World Hologram conjecture.

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