Thread: Alan Guth's inflaton, acceleration of the universe expansion rate, MOND and the fate of the universe

Presumably, when the universe formed from Alan Guth's inflaton, its graphical hyperbolic (proportional to 1/r*) gravitational field profile began to collapse into a parabolic (proportional to 1/r²) one (see posts elsewhere). This collapse or transition continues to this day. But surely, the process is almost done. There cannot be an infinite amount of gravitational energy sequestered in the hyperbolic 1/r* field that would be available to fuel acceleration of the expansion rate via such a transformation. That is, transition to a lower energy parabolic 1/r² field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the mainspring has almost run down by now.

If the expansion rate is called h, and its present value is called P, then h = P at any given time, t, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression,

P = h₀e^-rt, where h₀ is an initial value for the expansion rate, h, r is the rate of increase in this expansion.

We can get an estimate of a value for h₀ from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P₁, and acceleration rate, r, are observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = R₀e^rt, where R is the putative “radius” or scale factor of the universe.

The current value (at t = 1) of the expansion rate is H₀, the Hubble “constant”, so P₁ = H₀.

Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. The hyperbolic 1/r* graphical curve levels off near zero and continues to subside gently almost linearly for an indefinite time. The current state of the universe may be consistent with this dormant period. The conclusion here is that acceleration may continue for a long time while slowly decreasing nearer to zero. In other words, even with acceleration of the expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

The essential detail made about point masses and singularities engendering a hyperbolic 1/r* gravitational field is a mathematical necessity. Consider what a point mass as a singularity actually means. If it does not mean that they generate a hyperbolic gravitational field, then the words point-mass (remember Guth) and "singularity" are meaningless. Karl Schwartzchild would not agree with this negation of his analysis of general relativity.

Some say that general relativity predicts that black-hole singularities must possess a gravitational field that falls off as 1/r² with no difference from other Newtonian entities. I don’t believe general relativity says this under the rule that a black-hole must contain or “be” a singularity. If treated as a real singularity (see Schwartzchild metric, Wikipedia), black-holes must have hyperbolic 1/r* gravitational potentials. This is a geometric necessity.

Such a gravitational potential falls off as 1/r, or more accurately, as 1/r*. The symbol r* is the radial distance of a given star multiplied by the dimensioned value of the unit vector associated with the vector quantity of r, r which makes dimensional analysis valid in, say, F = GmM/r*. So, this is a hyperbolic equation.

The super-massive central black-hole, in association with the galactic disk which has a coincident and coaxial gravitational field equivalent to a couple of hundred billion sols, the residual hyperbolic 1/r* gravitational field at large r coincides with Milgrom’s tiny extra gravitational acceleration seen near the periphery of galaxies. The periphery is a self defining precise zone the relative location of which is responsible for Milgrom’s leftover acceleration “constant” that he wants to tack onto Newton’s Law. These observations mean that Milgrom’s MOND is unnecessary. And, Dark Matter as "quintessence" is superfluous too because all the characteristics associated with some deeply embedded Dark Matter phenomenon are explained equally well by the hyperbolic 1/r* galactic black-hole gravitational field effect. The “MOND effect” itself is evidence for the hyperbolic field.

The symbol r* is equal to r times the dimensioned value of the unit vector associated with r, r. It keeps the dimensional analysis of F = GmM/r* sensible. But, there are other fundamental reasons to use it.

What, it's not enough for you to not do physics in one thread, you have to start another thread in which you do not do physics? This is ridiculous. Do a god-damned calculation already or go see a psychiatrist.

Originally Posted by PhysBang

What, it's not enough for you to not do physics in one thread, you have to start another thread in which you do not do physics? This is ridiculous. Do a god-damned calculation already or go see a psychiatrist.

Exponential growth and decay equations are not physics? Look at my website LONETREE* PICTURES* &* NEW* COSMOS with MOND, subsite MOND. You may quibble with my presentation of funky looking whiteboard scribbles, but it is math. And it works. It should be accompanied by a lecture, however, because it is kind of hard to see what it means at just a glance. This lecture is now being promulgated by speakers bureaus in various parts of the country. Would you like a copy of my "one sheet" flyer?

I am already seeing a psychiatrist, thank you. Don't you?

You "do physics" your way, I'll do it mine. Logic is logic, whether by mathematics or spoken language.

This new thread has an entirely different thrust, being the fate of the universe. If all my threads were combined, no-one would bother to read them because it would constitute a book. I am sure that you would not object to this result, though. What if someone required you to combine your posts into a single tome?

Let's keep this up and give everybody a good laugh! We could give Jay Leno a run for his money. Be sure to see my hilarious joke about the hyperbolic (proportional to |1/rr|) black-hole gravitational field, posted above.

Originally Posted by Gary Anthony Kent

Presumably, when the universe formed from Alan Guth's inflaton, its graphical hyperbolic (proportional to 1/r*) gravitational field profile began to collapse into a parabolic (proportional to 1/r²) one (see posts elsewhere). This collapse or transition continues to this day. But surely, the process is almost done. There cannot be an infinite amount of gravitational energy sequestered in the hyperbolic 1/r* field that would be available to fuel acceleration of the expansion rate via such a transformation. That is, transition to a lower energy parabolic 1/r² field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the mainspring has almost run down by now.

If the expansion rate is called h, and its present value is called P, then h = P at any given time, t, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression,

P = h₀e^-rt, where h₀ is an initial value for the expansion rate, h, r is the rate of increase in this expansion.

We can get an estimate of a value for h₀ from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P₁, and acceleration rate, r, are observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = R₀e^rt, where R is the putative “radius” or scale factor of the universe.

The current value (at t = 1) of the expansion rate is H₀, the Hubble “constant”, so P₁ = H₀.

Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. The hyperbolic 1/r* graphical curve levels off near zero and continues to subside gently almost linearly for an indefinite time. The current state of the universe may be consistent with this dormant period. The conclusion here is that acceleration may continue for a long time while slowly decreasing nearer to zero. In other words, even with acceleration of the expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

The essential detail made about point masses and singularities engendering a hyperbolic 1/r* gravitational field is a mathematical necessity. Consider what a point mass as a singularity actually means. If it does not mean that they generate a hyperbolic gravitational field, then the words point-mass (remember Guth) and "singularity" are meaningless. Karl Schwartzchild would not agree with this negation of his analysis of general relativity.

Some say that general relativity predicts that black-hole singularities must possess a gravitational field that falls off as 1/r² with no difference from other Newtonian entities. I don’t believe general relativity says this under the rule that a black-hole must contain or “be” a singularity. If treated as a real singularity (see Schwartzchild metric, Wikipedia), black-holes must have hyperbolic 1/r* gravitational potentials. This is a geometric necessity.

Such a gravitational potential falls off as 1/r, or more accurately, as 1/r*. The symbol r* is the radial distance of a given star multiplied by the dimensioned value of the unit vector associated with the vector quantity of r, r which makes dimensional analysis valid in, say, F = GmM/r*. So, this is a hyperbolic equation.

The super-massive central black-hole, in association with the galactic disk which has a coincident and coaxial gravitational field equivalent to a couple of hundred billion sols, the residual hyperbolic 1/r* gravitational field at large r coincides with Milgrom’s tiny extra gravitational acceleration seen near the periphery of galaxies. The periphery is a self defining precise zone the relative location of which is responsible for Milgrom’s leftover acceleration “constant” that he wants to tack onto Newton’s Law. These observations mean that Milgrom’s MOND is unnecessary. And, Dark Matter as "quintessence" is superfluous too because all the characteristics associated with some deeply embedded Dark Matter phenomenon are explained equally well by the hyperbolic 1/r* galactic black-hole gravitational field effect. The “MOND effect” itself is evidence for the hyperbolic field.

The symbol r* is equal to r times the dimensioned value of the unit vector associated with r, r. It keeps the dimensional analysis of F = GmM/r* sensible.

I made more editorial changes that you might like, PhysBang. At least I think there should be less misunderstanding of where I am coming from.

I have prepared a One-Sheet for my lecture
on the Fate of the Universe

Many scientists have verified the fact that the Theory of General Relativity does indeed regard black holes as both physical realities and logical or mathematical subjects. Which means that they are real "point masses" (within Heisenberg limits) having infinite density and infinitely deep gravitational wells. This also means they have a graphical mathematical "asymptotic" limiting boundary (to both the abscissa and ordinate) gravitational potential profile. As such, their overall physical geometry must be consistent with their nature as singularities, or else the term "singularity" has no meaning. Their actual gravitational potential profile must be represented by a hyperbola. This is HUGE! Just how huge is the subject of my lecture.

This lecture is a Power-Point presentation. It is meant for the general audience of persons desiring an edifying talk on scientific subject.

I include many slides with beautiful graphics and photographs of a kind appropriate for a talk on astronomy. Stars, galaxies, planets, telescopes, people of science and their institutions, etc. Non-technical, it can be understood by any high school graduate.

I am a PhD level lecturer (graduated with a M.S. in physical science from I.I.T. in 1985) with a website http://www.lonetree-pictures.net, several popular blogs, respected participant in several scientific forums and a writer/editor for Wikipedia.

Please contact me if you would like more information.


Sincerely,


Gary Kent


Preview:

Albert Einstein easily derived a relativistic differential equation that was guaranteed to reproduce Newton's Law when it was integrated with certain simplifying assumptions. He could have written a differential equation that reproduced MOND, but he didn't. He just didn't. He had no reason to do so because the various MOND observations had not yet been made.

But, considering the very definition of a black-hole, it must be accompanied by a very characteristic and very different gravitational field. Because it is a singularity, a single point-object with infinite density, it must possess a gravitational field that is determined by its single point, its singular property. Its gravitational field graphical potential plot must therefore approach an asymptote (boundary line having a limiting value) at radius = 0 and, by symmetry, it must approach another (perpendicular) asymptote at radius = infinity. This is consistent with the definition of a hyperbolic field, not one that follows Newton's inverse square law, which is parabolic in nature. A hyperbola follows an inverse law, 1/r while a parabola follows an inverse square law, 1/r².

The Universe: HBH MOND - The Hyperbolic Black-Hole Field

If black-holes posses hyperbolic gravitational fields, then there is no mystery in MOND. Look at this image of a whiteboard derivation of the hyperbolic black-hole (HBH) gravitational acceleration and velocity profile near a galaxy containing a supermassive black-hole at its center. On the whiteboard, I also have written a synopsis of the MOND development:

Originally Posted by Gary Anthony Kent

... Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. The hyperbolic 1/r* graphical curve levels off near zero and continues to subside gently almost linearly for an indefinite time. The current state of the universe may be consistent with this dormant period. The conclusion here is that acceleration may continue for a long time while slowly decreasing nearer to zero. In other words, even with acceleration of the expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

The essential detail made about point masses and singularities engendering a hyperbolic 1/r* gravitational field is a mathematical necessity. Consider what a point mass as a singularity actually means. If it does not mean that they generate a hyperbolic gravitational field, then the words point-mass (remember Guth) and "singularity" are meaningless. Karl Schwartzchild would not agree with this negation of his analysis of general relativity.

Some say that general relativity predicts that black-hole singularities must possess a gravitational field that falls off as 1/r² with no difference from other Newtonian entities. I don’t believe general relativity says this under the rule that a black-hole must contain or “be” a singularity. If treated as a real singularity (see Schwartzchild metric, Wikipedia), black-holes must have hyperbolic 1/r* gravitational potentials. This is a geometric necessity.

Such a gravitational potential falls off as 1/r, or more accurately, as 1/r*. The symbol r* is the radial distance of a given star multiplied by the dimensioned value of the unit vector associated with the vector quantity of r, r which makes dimensional analysis valid in, say, F = GmM/r*. So, this is a hyperbolic equation.

The super-massive central black-hole, in association with the galactic disk which has a coincident and coaxial gravitational field equivalent to a couple of hundred billion sols, the residual hyperbolic 1/r* gravitational field at large r coincides with Milgrom’s tiny extra gravitational acceleration seen near the periphery of galaxies. The periphery is a self defining precise zone the relative location of which is responsible for Milgrom’s leftover acceleration “constant” that he wants to tack onto Newton’s Law. These observations mean that Milgrom’s MOND is unnecessary. And, Dark Matter as "quintessence" is superfluous too because all the characteristics associated with some deeply embedded Dark Matter phenomenon are explained equally well by the hyperbolic 1/r* galactic black-hole gravitational field effect. The “MOND effect” itself is evidence for the hyperbolic field.

The symbol r* is equal to r times the dimensioned value of the unit vector associated with r, r. It keeps the dimensional analysis of F = GmM/r* sensible. But, there are other fundamental reasons to use it. Note that with F proportional to 1/r, acceleration becomes constant at large r. This is MOND.

Revised and updated version of the above:

Origin, emergence and eschatology of the Universe: Dark Energy & Dark Matter

Should we mean “the universe” or “the meta-verse” or “the multi-verse”? (Hugh Everett)

Presumably, when the universe formed from an ensemble of some sort of “inflaton” point particles (Alan Guth) as a statistically inevitable child of an extremely excited field, possibly the gravitational field itself, its hyperbolic (proportional to 1/r - r is "radius" or better, scale factor) field began to collapse into a parabolic (1/r²) one. That collapse continues to this day. But, the process is almost done. There cannot be an infinite amount of energy sequestered in the hyperbolic 1/r field that would be available to fuel acceleration of the Hubble expansion rate by such a transformation. Transition to a lower potential energy parabolic field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the (1/r) potential energy mainspring has almost run down by now. The remaining (1/r) potential energy is called Dark Energy.

It accounts for the “missing mass ” and/or “Dark Matter” in audits of universe contents and provides a convenient, theoretically rigorous and parsimonious basis for “acceleration”. Dark Energy could account for around 80% of the universe’s total mass, but such audits are not so accurate. Dark Matter accounts for another 15% maybe. Still, The Mainspring may still have enough oomph to last for at least 140 billion years more! Assuming acceleration has gone about 1/10 of its course (it's exponential, you know... It is still almost run down). The total mass, including Dark Matter, of the universe is enough to “flatten” it while acceleration may creep to a stop, but Hubble expansion will not.

The hyper-excited gravitational field sprang into existence simply because it could, in Everett's Many Worlds. It came to be in a tremendously excited state because very high excited states are much more probable than lower ones, because of the zero point cut-off. This is just like quantum virtual particles that come to exist and be annihilated all the time on the sub-nuclear level (this is confirmed by experiment). None of them become universes, though, because there is already one here. It’s a sort of a Pauli exclusion principle.

There has been some confusion over "variable labels". So, let us switch definitions of r and be clear. In the following, r is the rate of acceleration of expansion of the universe (or rotational acceleration around a black-hole).

If the acceleration of the expansion rate is called a, and its present value is called P, then a = P at any given time, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression, P = h_o e^(-rt), where h_o is an initial value for h, r is the rate of increase in this expansion and t is time.

We can get an estimate of a value for ho from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P₁, and acceleration rate, r, is observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = R_o e^(rt),where R is the putative instantaneous “radius” or scale factor of the universe.

The current value of the expansion rate is Ho, the Hubble “constant”, so P₁ = H_o.

Back to our original definition of r (not using R) as a radius or scale factor:

Exponential decay equations exhibit what is called a “dormancy” period or late plateau region. In this part of the discussion, here, r refers to distance from a center of rotation.

I am really Sorry. I missed this inconsistency in previous posts. I need a nicer symbol for the exponential period, another name for r; maybe Cyrillic backward “R”? May be a lower case Cyrillic “r”?

The hyperbolic 1/r curve levels off near zero and continues to subside gently almost linearly for an indefinite time. Plot a graph yourself on the back of an envelope! Use mass M = 1, the smaller mass drops out for acceleration. And, assume G is any self consistent constant like G = 1 (units!). This is just for comparison purposes, so it matters not. See how the equation for orbital acceleration around a galactic center, say, levels off to a constant, even at infinity, for a hyperbolic 1/r black-hole galactic gravitational field potential diagram. (You have just DERIVED modified Newtonian Dynamics or MOND!) You must multiply r by the constant k = 1m (Systeme Internationale) for dimensional purity.

NOW, let us MIX the “r” metaphors. The current state of the universe itself may be considered as being in this (1/r) condition – mixing the two ways we define “r” - exponential decay dormancy or plateau period. The conclusion here is that acceleration of expansion may continue for a long time while very slowly decreasing nearer to zero. I really need a better, sophisticated looking variable symbol for one or the other "r"s. Maybe I already had it, plain old "R". Nah! Too mundane.

The black-hole rotational acceleration connection implies that the universe may be rotating very very slowly right now. But, we cannot know. We would have to observe the universe from the outside, from the perspective of the meta-universe, to tell. From the standpoint of general relativity, we simply cannot perceive it from our perspective here and now.

Yet, in other words, even with acknowledged acceleration of the Hubble expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

By the way, “M Theory” doesn’t exist. M Theory is just an “ideal”. Brane Theory is not M Theory. Neither has ever predicted anything that can be experimentally verified and neither is falsifiable. Therefore, they cannot qualify as legitimate scientific propositions. Not one single unique result has ever come from either. Furthermore, they are both unnecessary. Shrewd development of general relativity and quantum are slowly causing both to merge. What’s the hurry? Let true “M Theory” and “Brane theory” grow organically directly out of quantum and GR. Each step will be independently validated, then. No worry.

Origins, emergence and eschatology are fertile fields for philosophers. This is why we scientists are sometimes called “Doctors of Philosophy”, Ph.D. Doctori Philosophi. I took Latin for three years and I am still not sure of this. German and Russian too, but this is no help. What happened to my old Latin grammar texts?

This forum is a great place for an author to get feedback prior to submission of a manuscript to editors and referees!