Note to moderators:

This thread is an obvious rehash of the DEAILE/Duality threads. Nonetheless, the purpose is to:

1. Provide a clear, coherent synopsis of the duality model
2. Provide a single reference for the never-ending stream of newcomers asking—What-the-hell-is-Dark-Energy?—that I can point to and say, “Here is one possible answer; its not accepted by the mainstream, but no DE theory is. Have a look.”

The BA has said—paraphrasing—he won’t believe it until it’s published in a mainstream journal.*

I would try, but mainstream journals do not accept papers in plain English, and I lack the skills/resources necessary to translate it into scholarese. So here it is, for those who want to understand why the universe is expanding, and accelerating as it does so.

Note to readers:

Please do not post to this thread, per the spirit of BAUT rules on “discussion over.”

1. The dualistic model is pictured explicitly, below
2. The math is presented explicitly
3. The results are explicit: expansion energy is not a problem in this simple model
4. Its prediction is explicit, and can be tested by anyone with the requisite data-reduction/math skills

If you find an error in the paper which would change any number by more than a factor of 10, or have a question about where any of the numbers came from or how the calculation was done, PM me.

Thanks

*Mainstream understanding of duality coming soon!

__________________
PW -- Plant Whisperer

Comparison of a Quasi-Newtonian, Dualistic, Non-Singularity Expansion Model to Observations

Abstract

An estimate is made of the unit-power output of the visible universe due to on-going, local contraction. A quasi-Newtonian, dualistic expansion model sans singularity is presented, in which non-local (cosmic) expansion is exponential, and proportional to the rate of local contraction. The unit-power input required to expand this model at the observed rate is estimated. The power output of visible matter in the real universe is several orders of magnitude larger than the result of the estimate. This suggests we live in a universe whose fundamental characteristic is local gravitational contraction, and that the non-local (Hubble) expansion observed at immense distances is a residual effect. Non-local, accelerating expansion is predicted by the model, without exotic energy sources or new laws of physics.

Introduction

In Newtonian gravity, only the idealized 2-body system of point-masses in mutual orbit is stable for all time. In all complex, real-world systems, we can expect continual evolution of the system to be the norm.

The universe is said to be expanding, but this is true only on the largest scales. On local-scales, gravitational contraction dominates. As a rule, in gravitational systems more complex than 2-bodies, one part of the system will be contracting, while another part of it will be expanding. Therefore the answer to the question—is the system expanding or contracting?—depends on the lines of inquiry that we draw. This leads to the idea of duality.

Similar to the wave-particle duality in quantum mechanics, duality applied to cosmology says that whether a given gravitational system is expanding or contracting depends on which part we examine. When considering the universe as a whole, however, we cannot divide it. The visible universe is dominated by matter in a state of on-going gravitational contraction: it is unequivocally both expanding and contracting “at the same time.”

If we look at a main-sequence star, for example, we see the core is contracting (growing denser), but if we look above a certain radius—e.g. the photosphere—we observe that that portion of the system (the stellar wind) is expanding (growing less dense).

Finally, in any finite Newtonian gravitational system, expansion and contraction energy are well-defined. This principle of “well-definedness” is used here to compare the magnitude of local contraction relative to cosmic expansion in a quasi-Newtonian model of infinite size.

The results of this comparison show that local energy radiated away by visible sources is several orders of magnitude greater than the non-local potential energy gained via expansion. This is what one would require in a closed system, and suggests that the observed accelerating expansion of the cosmos is to be expected. That is, the Newtonian-approximation of infinity does not require an exotic energy source to explain the observed accelerating expansion.

Contraction of Obsered Universe

One can estimate the unit-power output of visible matter in the universe by dividing the radiant power output of a “typical galaxy” by its mass. The Milky Way galaxy has a visible mass of roughly 10^11 suns, with a dark component about 10 times that. It has a radiant energy output of about 10^11 suns. Using the figure of 4 x 10^26 watts for the sun and a mass of 2 x 10^30 kg, we have:

Power output of Milky Way = [10^11 sun-equivalent-outputs]*[4 x 10^26 watts/sun]/([10^12 suns]*[2 x 10^30 kg/sun]) = 2 x10^(-5) j/s/kg

Thus, on the assumption that the Milky Way is “typical,” the observed radiant power output of the universe, including dark matter, is roughly 2 x10^(-5) j/s/kg.

Quasi-Newtonian Dualistic Model

An infinite, quasi-Newtonian, dualistic model of the universe without singularity is shown in Figure 1. The sides of each cube represent the scale at which local gravitational contraction gives way to cosmic expansion. Roughly speaking, this is the distance at which the Hubble expansion overcomes local movement. Local velocity of galaxies relative to their (gravitational-bound) neighbors is +/- 200 km/s. Thus at 5 Mpc, the Hubble-expansion velocity is about 360 km/s, well exceeding any local motion. Therefore, 5 Mpc is used as a scale-distance for the model.

In the model, each cube is repeated in all directions to infinity.

Energy Source & Sink

Graphically, all local contraction (star and galaxy formation, etc.) is lumped together as a monolithic contraction of particles towards the center of each cube. The release of the 2 x10^(-5) j/s/kg as this on-going process occurs is not shown in the figure. Overall, the distance between each clump of matter is allowed to increase, hence the “quasi-Newtonian” label of the model.

The source and sink of energy in the model is shown in Figure 2.

The curve is the potential-energy vs. distance function, the ovals representing remote galaxy clusters. The 2 x10^(-5) j/s/kg observed power output is generated by matter "falling" down the curve on the left-hand side of the figure, off the bottom of the chart. Angular momentum prevents the in-fall from happening all at once, but matter continuously slides down the hill at the rate at which energy is radiated away.

Much of the radiant energy output of the universe can be attributed to nuclear energy, not gravitational potential. Nonetheless, in the model and the figure, nuclear and gravitational energy are lumped together. A star begins its life radiating pure gravitational energy; ignites the nuclear furnace at some point; and eventually reverts to radiating pure gravitational energy. The distance-function of the graph is really “average distance between baryons,” so in the nuclear-energy phase of a star’s life-cycle, the curve is steeper, that is, more nearly straight down.

At remote distances, where Hubble recession dominates, the curve becomes very flat, and greater recession velocity does not translate to higher energy-gain rate. In fact, by using the symmetry of the Cosmological Principle, all remote matter at all distances gains potential energy relative to all other remote matter at the same rate.

Thus, the source of energy in this model is pre-existing gravitational/nuclear potential energy. The cube in the top panel of Figure 1 has an inherent energy potential equal to Mc^2, where M is the total rest-mass of matter in the cube. This potential energy is transformed into kinetic and radiant energy as star and galaxy formation (local contraction) proceeds. Kinetic energy is retained within the cube, but radiant energy is lost “to space.” Simultaneously, the space between all cubes increases at the Hubble rate, resulting in exponential expansion. The bottom panel represents the model after about 2.5 billion years of evolution.

Expansion Power Estimate

The clump in the middle of Figure 1 represents our local group of galaxies at present time of on-going, local freefall. The dimension of cube is 5 Mpc, the distance at which Hubble expansion overtakes local motion. Density of matter is cosmic value, 3E-27 kg/m^3.

Side of the cube in meters:

5 Mpc*3.3E6 ly/Mpc*5.9E12 miles/ly*1600 m/mile = 1.6E23 meters.

The amount of matter in cube is:

(1.6E23 m)^3*3E-27 kg/m^3 = 1.1E43 kg.

Power output is:

1.1E43 kg*2E-5 j/kg-s = 2.3E38 watts

In Newtonian gravity, we cannot ask: how much energy does it take to increase the size of every cube? This is not allowed. Nonetheless, it is easy to imagine a Newtonian first-approximation. We can, in principle, calculate the power needed to expand any finite number of bodies using Newtonian gravity in Euclidean space, and look for a convergence. That is, we can calculate how much power is required to expand a 2-body system at Hubble rate; then we can calculate power required to expand a 3-body system; a 4-body system; etc. If we keep adding bodies in stable orbit around common center, the unit-power input required to expand the system into pre-existing space converges to some power requirement per unit-mass.

In this rough approximation, we go no further than the 2-body system, which will differ from the infinite-body answer by a geometric factor. That is, the 2-body system will provide an answer within an order-of-magnitude of the convergent value for an infinite-body system.

Consider two cubes in isolation, in mutual orbit, with the specification that this orbit is expanding at the Hubble rate. We employ the “spherical-cow” approximation and assume all the mass within the 2 cubes is concentrated in 2 point-masses in mutual orbit. Distance between them is the dimension of the cube, 5 Mpc or 1.6E23 m.

Force between clumps, using F=G*m1*m2/r^2=

6.7E-11 N-m^2/kg^2*(1.1E43 kg)^2/(1.6E23 m)^2= 3.5E29 N

Power is force times velocity (velocity of expansion), and expansion velocity is Hr:

P = 3.5E29 N*5 Mpc*72,000 m/s/Mpc = 1.3E35 watts

On per-kg basis:

1.3E35 watts/2.2E43 kg = 6E-9 j/kg-s

In other words, using simplest approximation we can imagine—a finite-mass Newtonian universe consisting of only 2 “particles” (2 galaxy clusters) in mutual orbit—the energy—1.3E35 watts—required to expand such a system at the Hubble rate, is about 1,000 times less than the radiant energy output of that same universe. The energy required to expand the model is insignificant in comparison to the energy lost by contraction.

Relation of Model to Observations
(Courtesy Sylas)

The Hubble flow is the rate at which distant galaxies are receding. It is often given in km/sec/MegaParsec; and it can also be given in units of inverse time. It is, by definition, equal to "(da/dt)/a"; the rate of change of scale factor (a) divided by scale factor. In a homogenous and isotropic universe, at any point in time the scale factor, and the rate of change in scale factor, is fixed throughout space. However, they can both change with time.

In this model, the scale factor is an exponential function of time. That is, da/dt is proportional to a, and so the Hubble flow rate H is constant. However, H is not truly constant, but changes with time, so we have H(t). H(t) is proportional to the rate of radiant power output P(t), which is slowly decreasing with time.

To fit the model to observations, H must decrease about 3.6% per billion years. With some effort, a unique plot of H-vs-time (H(t)) came be made from the Super Nova observations. The specific prediction of this model is that the resulting “best-fit” of H(t) will match the decrease in star-formation rate determined by independent means. Or more specifically, the H(t) determined from the observations by this model will be proportional to P(t), the power-output of the visible universe with time, as proposed in the model.

Conclusion

Duality works in this Newtonian approximation. It works because there is no horizon problem; there is no flatness problem; there is no singularity problem; there is no age crisis; no missing monopoles; no energy shortage; the Hubble “constant” is changing in the right direction (decreasing), that is, the changing in the direction required by the model.

A more vigorous analysis of the data may make or break the model’s quantitative prediction. And skeptics will complain that it does not encompass General Relativity. Nonetheless, every visible object in the sky—with the most trivial of exceptions—is in a state of on-going gravitational contraction. It is neigh impossible to imagine that all this "action" can fail to have a reaction. In order for local contraction to not be the cause of cosmic expansion, we must toss out one of physics’ most fundamental tenets: action-reaction.

The universe must be expanding—according to this Newtonian-based duality model—because it’s contracting.

__________________
PW -- Plant Whisperer

Why can't we post to the thread?

plus if it's just a rehash of an already closed thread how do you expect it to stay open if you aren't presenting anything new?

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All Moderation in Purple

I'm trying to stay out of trouble with the mods!

Its already been hashed out at length here and there.


I don't. It's only purpose is to provide a clear, coherent synopsis of the duality model:
here's the model; here's the math; here's its prediction.

The BA won't accept duality...because its not published in a mainstream journal. The mainstream journals won't accept it...becuase its written in English. Verifying the prediction requires math skills beyond my ability.

As near as I can figure, my only option is to wait until duality is published in a mainstream journal...and then try to get credit after-the-fact: Hey!!! I published the duality model on BAUT first , here!!!

Any other suggestions?

__________________
PW -- Plant Whisperer

I don't have a suggestion, but I do have a question: People who have mastered the necessary math skills don't seem to be very enthusiastic about duality. Why do you suppose this is?

because it has to be written in English?

__________________
All Moderation in Purple

Because it's not mainstream?

__________________
PW -- Plant Whisperer

I think you misunderstood my question. Let me rephrase it:
Why do you think those who have mastered the necessary math skills are reluctant to accept duality into the mainstream of physics?

Is there a mistake in my math?

__________________
PW -- Plant Whisperer

I have no idea if there is a mistake in your math. However, you yourself said that you don't have the math skills to verify your predictions:
When you said this, it prompted in my mind the following train of thought:

1. Peter Wilson is promoting a theory of physics that makes predictions.
2. These predictions require a certain minimum level of math skill to verify.
3. I assume that there are a great many mainstream physicists who have the required minimum level of math skill to verify such predictions.
4. Few (none?) of these physicists seem to think that their knowledge of math justifies the theory that Peter Wilson is proposing.
5. What reason does Peter Wilson give for this lack of enthusiasm for duality, among people who have the math skills Peter Wilson lacks and which are necessary to support Peter Wilson's theory?

stutefish:

I cannot answer for other people.

If you think there is a flaw in the theory, show me. Otherwise, there is nothing to discuss!

100 years ago, people ridiculed scientists who proposed that dinosaurs were wiped out by a giant asteroid impact. But 100 years of ridicule did not undo the theory…because it works.

Duality has been on the BAUT board for over a year, and while "mistakes were made" (and mostly caught) in the original exposition, no one has found a fatal flaw. Nereid has complained that duality does not explain the cosmic microwave background; nor the nuclear isotope abundances; nor why Paris Hilton is so popular Valid, legitimate considerations but not enough to undo the theory...because it "works:" duality gives correct answer to the problem it addresses.

I opened the present thread with “something new,” as per the spirit of BAUT regulations: I boiled 2 long, rambling threads with 367 posts between them into one, coherent 1900 word “paper” explaining the duality model as clearly as I can. The model does not include GR, but the Earth’s tides are explained without recourse to GR.

The math and model do not go beyond first-year physics and math. While I do not expect everyone on the board to be proficient with 1st year math & physics, ridiculing a theory because it has not yet attained wide-spread acceptance does not count as “something new.” So either find a mistake, or find another ATM thread to post in.

In other words, put up or shut up

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PW -- Plant Whisperer