Jason,
I watched a you-tube of Tajmar explaining his experimental results to an audience. After discussing the ring laser gyro measurement of the C-field he asked:
"What can cause a frequency shift of photons."
Right down your alley.
Edwin Eugene Klingman
Hi Edwin,
I guess a ring laser gyroscope "would" be able to detect rotation of the ring. I think that fiber optics are effectively mirrors on the inside (along the bore of the fiber optic cable; in addition, there is glass or some kind of material with index of refraction n>1. I think it's cool that the rotating ring would almost act like mirrors that are moving towards/away from photons that bounce of the walls of the fiber optic cable. The fact that the "moving mirror effect" doesn't produce redshift or blue-shift is amazing AND something I'll need to think about.
I've got a question for you. At the momentum of the Big Bang, why didn't the gravity associated with all that energy cause the Big Bang to become a gigantic black hole? Unless you have a better answer, consider this answer. Gravitational potential has a slow reaction time. Space-time needs time to curve space-time in response to an excitation. In other words, at the moment of the Big Bang, gravity (space-time curvature) had not yet reached the equilibrium. Gravitational potential has a 1/r dependence. But how can a curvature travel all the way out to an infinite distance r inside of a nanosecond? It can't. In effect, gravity was still putting on its boot when the Big Bang explosion was riding off at light speed.
Remember that gravitational potential can only propagate at the speed of light. Photons move at the speed of light, and were laughing at gravity which couldn't get its act together quickly enough to produce a black hole. Gravitational potential is NOT instantaneous. However, it's expected to induce a proper gravity field instantaneously. Poor gravity; expectations exceed capability.
Why do I belabor this point? Because it means that the Einstein equations can't keep up with a rapid enough change in energy. If true, then the Einstein equations are no longer carved in stone. The Einstein equations are mortal and they can be defeated. Space-time will try to conserve energy. But if it's response time is too slow, then energy conservation can be violated. Eventually, gravity will catch up and plug up the leakage of energy; in doing so, space-time will curve to compensate for the additional energy (after it's gotten its boots on). Space-time curvature has to clean up the mess by achieving the proper gravity. Gravity complains and mutters with irritation that it has to go out to r = infinity to achieve a balance between energy and gravity. Gravity calls energy (photons) irresponsible and inconsiderate of consequences.
What's my point? Gravity is obligated to uphold the Einstein equations. I'm tempted to call it a mandate of God, but that would be a distraction. Control systems describe how a system will try to dampen out an excitation. What is gravity's control system in order to re-achieve the Einstein Equations? I don't know either, but I think we should look for poles and zeroes of gravitational space-time. In electronics (and control systems), the system has a transfer function of the form,
[math]H(s) = \frac{K(s-z_1)}{(s-p_1)}[/math]
H(s) = \frac{K(s-z_1)}{(s-p_1)}
I'm willing to bet that the shift photon is such a pole. I think its frequency will be the repetition rate of the shift photon.
If I'm right, then we just jumped ahead 500 years technologically.
Jason,
Yes, and the most interesting thing to me is that a static ring laser gyro detects the circulating C-field (the rotational aspect of gravity.)
Your next question is tricky. If we agree on a Free Lunch Universe, then the outward kinetic energy of motion must equal the inward potential energy of gravitational attraction. I never understood how the universe was supposed to inflate much faster than the speed of light, but I think that falls within the 'scale invariance' discussed in my essay. As Ray Munroe made me aware, Nottale shows that 'scale invariance' is the same as 'motion invariance'. As I conceive of this the 'shape' of the potential is preserved whatever the scale, so that a rapidly expanding universe that is independent of scale is also independent of motion and hence the speed of light. This seems to be what you are talking about: "gravity was still putting on its boot when the Big Bang explosion was riding off at light speed."
It's difficult to grasp these special conditions intuitively, but they seem to be implied by the Free Lunch assumption, and my Master equation is definitely scale invariant.
I understand control theory and transfer functions, but not all systems try to damp out excitations. I don't quite see how the shift photon does this.
Edwin Eugene Klingman
Hi Edwin,
I'm just not getting the scale invariance idea.
This is a little frustrating for me, but I figured out the Big Bang/gravity potential thing. In the first few minutes of the Big Bang, the energy density is homogeneous, therefore, the negative gravitational potential is negative and and flat (no gravity fields yet). The effects of gravity are irrelevant because there is no slope. However, the poor SOB on the outside of the Big Bang who didn't see it coming, he suddenly gets (1) severely irradiated with energy and (2) falls into a precipitously steep gravitational slope at the outer edge of the Big bang; suddenly that poor SOB is part of universe universe now. As the universe expands, the energy density gets less and less. The gravitational potential also gets less and less. The gravitational potential remains flat until matter forms and starts to clump. Eventually, the negative flat gravitational potential energy inside of the universe gets less and less negative until it equalizes with the space-time that was already here. So, in a way, the Big Bang created a whole new universe, but it quickly became part of the old universe that was already here. The Big Bang didn't become a black hole because the gravity well was flat, not sloping inwards; well, the slope was vertical with the old universe; equilibrium had not been reached. At one point, maybe in the first pico-second, the energy density was high enough to be a black hole. FTL phenomena is permitted inside of black holes.
This is really frustrating for me because I want to explain how the Einstein equations can only respond at the speed of light. Unfortunately, the Big Bang has to hide this fact by maintaining constant density.
So just imagine that a giant neutron star just pops up from out of nowhere. It doesn't explode at the speed of light because it has a constant diameter. However, its gravity field expands outward at the speed of light. As the gravity field expands outward, there will be longitudinal gravitational ripples in space-time. These ripples get damped out very quickly.
Yes, I know this has never happened before. It's a thought experiment. Yes, I understand that the neutron star would probably explode anyway because of the gravity waves. How about a gigantic ball of Pb (lead)? Along the radii of the giant sphere made out of lead (Pb), the gravity waves would radiate outwards as attraction and repulsion. Time would slow down and than speed up again. There would be spherical wave-fronts of attraction and then repulsion. You could model these gravity waves with a sinusoid...
[math]g(t) = g_0 cos (\omega t)[/math]
g(t) = g_0 cos (\omega t)
Shift photons have a constant potential energy slope; yes, it's repeating, but at a high repetition rate, it looks like a constant gravity field in one direction.
Work with me...
Dear Sir,
your essay was very interseting to read! Congratulations!
As I am not an expert in these theories I have a (possibly trivial) question.
You mentioned at pg.5 a final assumption for deriving real particles, distinguishable from real fields: That the curvature of space is limited. And as consequences of this, that electrons and quarks and also black holes appear as limits.
My question is: If you have a limit for the curvature: is this a natural constant or could you also chose a half or a quarter of this number and guarantees also a limited curvature?
Best regards
Niklaus Buehlmann
Niklaus,
Thank you for your comment and for an interesting question.
While the process effectively provides a 'limit to curvature' the term itself may be more metaphorical than accurate. What happens is this:
The equivalent mass of the vortex wall, interacting with itself, produces a solenoidal C-field, just as an electric charge current produces a solenoidal magnetic field. But the increased C-field has the effect of forcing the vortex wall toward the central axis, while conservation of angular momentum increases the speed of the vortex wall. Where does this end? If an ice skater could pull her arms in all the way to a zero radius, how fast would she spin?
This is not a 'boost' situation, such as occurs in relativistic linear acceleration, so there is no natural limit, and no reason to assume that the vortex wall velocity will not reach the speed of light. If it does, what happens? I conjecture that electric charge is created at the v=c point in the process. As it turns out, the equations show that the point where this occurs is the Compton radius of the electron, that is, the 'size' of the electron as observed by electromagnetic radiation. This does not stop the vortex wall from shrinking to a point, but now there is a 'braking force' at play, since the self-repulsion of the charge increasingly resists the shrinking.
You ask about a 'natural constant' associated with this process. If one sets the C-field inward force equal to the charge self-repulsion outward force, then the point at which they are equal (and presumed stable) yields the fine structure constant, which is currently derived in no other theory.
And this 'stable' size is of the order of 10^-18 meters, a thousand time less than Compton wavelength. So the electro-magnetic field sees one size, that is associated with the v=c wall velocity, while particle collisions see a much smaller size that is associated with the final stable radius of the particle. Note that all electrons are 'identical' since one cannot even in theory observe a 'mark' on one, as the mark would move away faster than c.
This conjecture as to how charge comes into the picture is the weakest point of my theory, but compare it to string theory in which each 'winding' of the string through a 'hole' in an 11-dimensional Calabi-Yau manifold produces one unit of charge, and it doesn't appear so unreasonable. And QED simply conjectures that quantum fields, operating at a point, produce charge, but without mass, which requires a Higgs field.
I hope that explanation gives you a better picture of the process that I metaphorically described as 'limit of curvature'. It actually does limit the curvature of the C-field vortex wall, but it is due to the self-repulsion of the charge equaling the inward force of the C-field on the vortex wall.
Edwin Eugene Klingman
Jason,
Look at the first figure on page two and again at the figure on page 7. The red curve is the (2D graph of) the G-field potential. Note that it has a 1/r distribution. What this means is that the energy density is NOT homogeneous, but peaks at the r=0 (singularity?) and decreases as one moves away from this.
Since you state that "In the first few minutes of the Big Bang, the energy density is homogeneous," then any conclusions that you draw from this will not apply to my theory, but, as seen on page 7, will apply to the FLRW solutions to Einstein's General Relativity 'dust' equations that do assume homogeneity.
I don't know how to explain 'scale invariance' other than that if one multiplies the solution by a scale factor, it is still a solution of the same field equation. This is worked out in my appendix C. The Nottale references (thank you Ray) are in my list of references.
You also say: "This is really frustrating for me because I want to explain how the Einstein equations can only respond at the speed of light. Unfortunately, the Big Bang has to hide this fact by maintaining constant density. "
Again, there is no 'constant density' in my model.
Edwin Eugene Klingman
Hi Edwin,
After the inflationary epoch, quarks and gluons start to form; that throws a monkey wrench into the model. Quarks and gluons make up protons and neutrons (which are matter), which can't keep up with light. So gravity is an issue now.
I'm trying to understand what you mean by low entropy. Since it might be the case that hadrons can't keep up with photons, then hadrons fall behind. If the explosion is outwards (like a grenade), then the gravity and light lead ahead of the particles (outwards), and a gravity field can develop.
However, if there is no center because the Big Bang is a 4D space-time hypersphere (subtle sarcastic use of the word hypersphere), then the gravity field and photons are moving faster, but are not leaving particles behind. It's like bringing 50 obnoxious ADHD kids to a nursing home and locking the doors. The kids move really fast, the old people move really slow, but the kids never move away from the old people because the doors are locked. If the Big Bang is such a 4D hypersphere, then the energy density IS the same everywhere in space.
Your figure on page 2 suggests geodesics that I can't even imagine. Yet I think you are suggesting that there is no geodesic caused by the expansion of space-time. In your paper, you said, "Yet most field-energy-mass of our G field is near the singularity, thereby achieving the required minimal entropy:"
It sounds like we both prefer the grenade effect where the center (r=0), is somewhere rather than everywhere (for those who like hyper-spheres).
There are quite a few points of discussion. I don't know if there was a pre-existing universe or a gravity discontinuity moving out at the speed of light from the Big Bang center. It's a thought experiment worth considering. What I'm after is whether or not gravity/space-time has a resonant frequency and a transfer function that I can use to overcome gravity. Call me crazy, but I'm looking for an H(s) that is the quotient of the output divided by the input. The input is a sinusoidally changing frequency (like FM radio with a sinusoid input). The output is a gravitational disturbance. Obviously, this resonant frequency is not 88 to 108 MHz or we would have noticed. Tunable lasers look more hopeful, but 5000 repetitions per second is apparently not fast enough.
By the way, the frequency is
[math]f= \frac{d \theta}{dt}[/math] f= \frac{d \theta}{dt}
So what should I call df/dt? Chi?
[math]\chi = \frac{df}{dt}[/math] \chi = \frac{df}{dt}
Jason,
Willard has made me want to recheck my statements about entropy, and I have not yet had a chance to do so. But regardless of this you are correct in your statement that "hadrons can't keep up with photons, then hadrons fall behind".
You say: "If the explosion is outwards (like a grenade), then the gravity and light lead ahead of the particles (outwards), and a gravity field can develop." But the gravity field is already developed. Gravity is the one and only primordial entity in my model. The rotational aspect of gravity (the C-field) appears only after symmetry is broken, then neutrinos appear, then neutrinos interact with the boson/vortices and produce electrons and quarks. These particles bring charge into the picture and then photons appear. It may not be the order that you want things to happen, but it's what my model predicts. At that point we have every particle that is known today, as well as forces that explain the current phenomena and the exceptions/anomalies to other theories.
You then say: "then the gravity field and photons are moving faster, but are not leaving particles behind." But I would expect the gravity and photons to leave the particles behind (although the neutrinos will be moving almost light speed.)
As for "Your figure on page 2 suggests geodesics that I can't even imagine. Yet I think you are suggesting that there is no geodesic caused by the expansion of space-time. In your paper, you said, "Yet most field-energy-mass of our G field is near the singularity, thereby achieving the required minimal entropy:"
This is a 2D representation of the gravitational field strength before symmetry breaks. Think of it as very highly stressed space in which almost all of the gravitational field strength (and hence equivalent mass) is at or near the origin, r~0. I interpreted this to imply low entropy, but I need to study that statement.
"It sounds like we both prefer the grenade effect where the center (r=0), is somewhere rather than everywhere (for those who like hyper-spheres)." Yes, I definitely have a 'center', not a hypersphere.
As for "There are quite a few points of discussion. I don't know if there was a pre-existing universe or a gravity discontinuity moving out at the speed of light from the Big Bang center. It's a thought experiment worth considering." I'm not really sure that it's a thought experiment worth considering. Many men that were smarter than you and I have discussed what came before the universe, and no one has answered the question. Certainly the bouncing universes I see today make no sense. They only push the problem back before the first bounce. John Merryman's (and others) eternal universe is no easier for me to understand, and does not produce the various ingredients that my model produces ( or if it does, he doesn't tell us how.)
"What I'm after is whether or not gravity/space-time has a resonant frequency and a transfer function that I can use to overcome gravity. Call me crazy, but I'm looking for an H(s) that is the quotient of the output divided by the input. " I don't think you're crazy. You're one of the most imaginative guys around. And all ideas sound crazy initially, at least to those who believe in the current consensus. Yet there really does seem to be a physical reality (though some here think there's only math or virtual reality) and at some point our theories and new ideas must match the reality. I think your question about the resonant frequency of space is a wonderful question, but I suspect that, since the big bang provided the 'mother-of-all-impulses' that the system would already have been driven into resonance, and we should at least see some remnant of that behavior, assuming that it damped out due to inflation (or something).
I like the way you hold on to your idea like a bulldog. That's the only way to reach the end. Of course the end is likely to be a disappointment, but you never know until you get there.
Edwin Eugene Klingman
Hi Edwin,
I wrote a story on
http://www.fqxi.org/community/forum/topic/647
It's about the planet Maldek that built a Big Bang bomb energy weapon and, well, you can just read the story. I describe how the bomb was made.
The oscillating universe (expanding/contracting) just sounds too contrived to me. A pre-existing universe with a very rare Big Bang event seems more natural. Did God cause the Big Bang, was it a natural phenomena or the ultimate weapon? It's left to everyone's imagination and preference. But the idea solves the conservation of energy dilemma.
"The rotational aspect of gravity (the C-field) appears only after symmetry is broken, then neutrinos appear, then neutrinos interact with the boson/vortices and produce electrons and quarks. These particles bring charge into the picture and then photons appear. "
I want to applaud you for taking a stand on C-field gravity physics. Making specific predictions exposes a theory to attack; only the correct theory survives. All the rest of us get to experience the anguish of seeing our prized and beloved theory die. Lots of theorists hide their ideas in 10 dimension string theory space because they can't endure the pain. In a way, it's like robot wars.
http://en.wikipedia.org/wiki/Robot_Wars_%28TV_series%29
The trick to building a good theory is to use as few parts as possible; and work with the parts of the theory that survived the last battle.
And if C-field theory survives and photon theory dies, I will cry first, and then quickly adopt C-field theory. I just want to be right going into the next battle.
I'm taking a closer look at Frequency Modulation as a solution to a gravity field Transfer function. My instincts tell me that the fastest repetition rate possible is the answer. When I can write down the transfer function, input and output, I'll post it.
Congratulations Edwin! You made the front page. Just click on HOME to see it. Well done.
Hi Edwin,
I need to draw a picture to show you this. The Big Bang was an energy conserved event because a gravitational potential (negative energy) and an explosion of light (positive energy) both exploded outward at the speed of light. Both add to zero.
But there is another energy conserved event. Photon Theory says that everything in physics can be decomposed into photons and wave-functions. Here is an example of a gravity wave-function.
A space-ship produces
(1) a negative energy gravity wave that travels to the left, and
(2) a positive energy gravity wave that travels to the right.
The spaceship is supposed to ride the negative energy gravity wave. If it rides the positive energy gravity wave, it falls off and gets left behind.
If the space-ship is too big, the gravity wave leaves it behind. If the space-ship rides inside the negative energy gravity wave, it will literally travel at the speed of light for as long as the space-ship remains inside.
It's not a hyper-drive, but the speed of light is still pretty quick.
I need help with the the details. What do you think?
Dear Ed,
Your Master Equation seems to generate the correct types of fields, but I am concerned that these limited fields (G,C,E,M) in 4 dimensions do not contain enough degrees of freedom to account for all known generations of "fundamental particles" - at least an SO(10) of fermions and an SU(5) of bosons. You begin with continuous fields only, and try to insert quantized "fundamental particles", but you omitted talking about Second Quantization, and this is the most accepted method for obtaining quantized particles from continuous fields. I also didn't discuss Second Quantization in my essay, because I proposed that fields and particles are both necessary complementary inverse scales.
Tajmar's explaination of a mass increase in Niobium Cooper-pairs is interesting. Superconductivity has also been implied to be the bridge between electromagnetism and gravitation by Chiao's and Podkletnov's research teams. You mention a kappa ~ 10^31, but Chiao says that a gravitational wave should have an effect of 42 orders in magnitude. I agree with Chiao because this is of order Dirac's Large Number ~ 10^41, which is one of my scale numbers (please see Equation 15 of my book for the relationship between electromagnetic and gravitational couplings). Now we can explain the Cosmological constant of Lambda ~ 10^(-123) ~ (10^41)^(-3) by the fact that we have three spatial dimensions (you said "If scale invariant is motion invariant, time has no obvious meaning"). I think that your inverse square-roots (~10^61) and inverse fourth-roots (~10^31) of Lambda should be replaced by inverse cube-roots (~10^41 - Dirac's Large Number) or by new modeling.
By the way, this variance in Niobium Cooper-pairs is fairly small. A change in the application of Statistical Mechanics may make-up this difference. Please contrast my Prespacetime Journal volume 1 issue 9 paper with Chapter 4 of my book.
You said that the "curvature of space is limited". I agree. At some energy level, we will promote matter-anti-matter pairs out of the Dirac Sea, and this may have a lattice-like "pinching off of Spacetime" effect. I propose that the core of a static black hole may be surrounded by a Buckyball (a nearly spherical lattice that has lattice bonds to resist it from being deflated by the gravitational near-singularity) consisting of the very fabric of Spacetime. The curvature of the Buckyball initiates Spacetime curvature. There is a smooth homotopy between a pair of nested Buckyballs and a lattice-like torus (donut), and this application may be appropriate for rotating Black Holes. In fact, normal Carbon fullerenes (such as the Buckyball) may have superconductor characteristics. Is the Black Hole core a Superconductor? If so, then a rotating superconducting GEM torus would produce a powerful dynamo. That would tie your ideas, my ideas, and Tajmar's, Chiao's and Podkletnov's ideas together...
I still disagree about 4 fundamental particles, but your field approach is interesting...
Have Fun!
Dr. Cosmic Ray
Ray,
Thanks for taking another look at my essay, and for checking out Tajmar.
I believe that he's backed off in his interpretation of the Cooper pairs as the source of the gravito-magnetic field. Not his measurement data, just his explanation of its source.
I'm not sure what is meant by 'bridge between electromagnetism and gravity', and I do not believe that gravito-magnetism is related to electro-magnetism other than through the similarity of their respective field equations. It seems to be the case that our universe supports both radial forces and 'deflective' or circulation-type forces, and this applies whether it's mass or charge sourcing the fields.
As for the energy of the cosmological constant, if the energy is that of the C-field, then we would expect it be proportional to the C-field squared, and thus lead to C~10^61. If 3 dimensions come into play I would expect this to lead to a factor of 3 (such as kT~(3/2)mv^2) rather than a cube root, but maybe I am missing your point.
I do not attach much significance to the Niobium Cooper pairs (and I think Tajmar has backed off of that explanation). He has detected the C-field dipole for other materials as well.
You agree that 'the curvature of space is limited'. Did you notice my response to Niklaus above (Feb. 13, 2011 @ 20:13 GMT) expanding upon that sentence.
You conjecture that Buckminsterfullerenes may have superconducting characteristics. I would not be at all surprised. As for Black Holes cores, I don't have much of an opinion there. But rotating Black Holes should produce one hell of a C-field dipole, which I interpret to be the mechanism behind the light-years-long jets emanating from such holes.
I'm all in favor of our ideas working together, and I'll address your disagreement about 4 fundamental particles in a later comment.
Thanks again for looking at my essay. In the last few days we've all got a lot more essays to look at.
Two that I especially like are Julian Barbour's 'Bit from It' and Patricio Valdes-Marin's "Structure and Force".
Edwin Eugene Klingman
Jason,
I just want to acknowledge and thank you for this comment:
"I want to applaud you for taking a stand on C-field gravity physics. Making specific predictions exposes a theory to attack; only the correct theory survives. All the rest of us get to experience the anguish of seeing our prized and beloved theory die. Lots of theorists hide their ideas in 10 dimension string theory space because they can't endure the pain."
That was a very kind thing to say. And it is also admirable of you to state:
"And if C-field theory survives and photon theory dies, I will cry first, and then quickly adopt C-field theory. I just want to be right going into the next battle.
Edwin Eugene Klingman
Jason,
You ask what I think, so here goes.
I am not at all convinced that 'gravity waves' exist. I listened to Joseph Weber circa 1970 lecture on his first gravitational wave detector, and it's been a long dry 40 years since, with no waves detected, despite that Russell Hulse and Joe Taylor were awarded the Nobel Prize in Physics.
You also state: "Photon Theory says that everything in physics can be decomposed into photons and wave-functions."
I believe that photons are physically real and that wave-functions are a mathematical description and are not physically real, so it's difficult for me to help design a system that contains (from my perspective) real and imaginary parts.
So without intending to discourage you in any way from sticking with your Shift Photon idea, I won't be much help for positive and negative energy gravity waves traveling away from a source. If the 'negative wave' were strong enough for the ship to 'ride it', it would probably induce destructive tides in the ship.
But you continue to display the most fertile imagination in sight.
Edwin Eugene Klingman
Ray,
This reply follows the comment below.
You are concerned that "the limited fields (G,C,E,M) in 4 dimensions do not contain enough degrees of freedom to account for all known generations of "fundamental particles" - at least an SO(10) of fermions and an SU(5) of bosons."
There are only three known generations (and closure of CKM seems to imply that's all there ever will be) and my model produces these three generations.
Then you say "You begin with continuous fields only, and try to insert quantized "fundamental particles", but you omitted talking about Second Quantization, and this is the most accepted method for obtaining quantized particles from continuous fields. I also didn't discuss Second Quantization in my essay, because I proposed that fields and particles are both necessary complementary inverse scales."
Ray, I do not take Second Quantization to be physically real, but only an algebraic approach to "creating" and "annihilating" ideal 'particles' at a 'point'. Nothing real there as far as I'm concerned. I believe I mentioned (on your thread) that my Masters thesis treated the shift in energy levels of an F-center (an imaginary atom formed by an electron trapped in a negative ion vacancy of a crystal). The shifts were due to the interactions of the phonons with the 'atom', and I treated this using Second Quantization for the phonons, but I do not really believe that "quantum fields" exist that create and annihilate phonons, nor do I believe that to be true for fundamental particles.
That's why I don't mention Second Quantization.
Edwin Eugene Klingman
Ray,
More specifically, with regard to Second Quantization and phonons: As is true for any system near equilibrium, phonons can be viewed as 'oscillations' and Second Quantization is simply an algebraic technique for adding and subtracting oscillations as one wishes. The same technique turns out to be useful for particles. For an excellent treatment see Anthony Zee's text: "Quantum Field Theory in a Nutshell". He remarks (after using a 'mattress' as a model) that "even after 75 years...quantum field theory remains rooted in this harmonic paradigm."
There's a reason for that.
Edwin Eugene Klingman
Dear Edwin,
I am not a professional physicist. I am only Scientific American reader. So your essay (maybe very good one) is too complicated to understand and evaluate. Too much equations and professional jargon.
Anyway I wish you good luck!
Walter John
Dear Walter,
Thanks for the feedback and for your kind wishes.
