a-cosmology-group/acg#122

Ethan Siegal: Official stance is always correct. Einstein’s Theory is always victorious. Criticism on official science is always wrong.

Anyhow, he has one correct point. Wide binaries are located within the galaxy.

As we go to very wide separations, even if your binary stars remain gravitationally bound, how are their accelerations influenced by both the presence of potentially massive Oort clouds (especially if the stars are young and massive) and by the background density of dark-and-normal matter that permeates the Milky Way? The assumption is “not at all,” but that may not be correct.

On the whole, he himself is doing bad science. Many years before I just first time interacted with him on his twitter post. Off course I just somewhat criticized his points. Then my twitter account was permanently suspended with no right to appeal.

Forbes, Twitter (of that time) and Medium are / were running on same policy. To keep this clown science communicator safe from any criticism.

@khuramonline I’ve never used the Musk melon formerly known as Twitter but I criticize Siegel on Medium often. I take care to avoid ad hominem remarks and I have never had a problem. I understand your reason for calling him a “clown” but if you use that kind of language in your criticism on well-run public forums you will get banned. See my critique here for example:

https://medium.com/starts-with-a-bang/jwst-at-last-answers-our-biggest-cosmic-questions-5e3881f33d6

I had written on his tweet something like … Your theories suggest that you know how many angels are dancing on a pin nib. I had used these types of words. I also used words that included medieval ages because that problem of angels dancing related to that era. When i commented that, at that time Elon Musk was not the owner of twitter.

He could tell and he always keep on telling that he knows exact number of angels dancing on a singularity point. Off course he is not ‘cl**n’ by his profile picture.

If I used bad words, they banned me. But I stand by my words. He and his directors have made science into a proper cult.

Have seen your comments there. Good to see that you also had same complaint against him as I had. Your words were humble but you also used word cult for him. My harsh words can have other reasons … like my fight experience with other cults.

a problem arises, which is the implication that MOND accelerations are vector addable Does this make sense?

Yes, I think that it makes sense.

Let’s quote from the Wide Binary paper at 5.3, emphasis by me: >Finally, the clear gravitational anomaly suggests that MOND is realized by modified gravity rather than modified inertia. [ .. ] modified gravity seems favored, although the work has not directly distinguished between modified gravity and modified inertia.

Maybe this must be interpreted as: modifying $\vec{F} = m\vec{a}$ is different from modifying Newton’s law of gravitation.

Variable Mass theory

I have another proposal - no surprise: it’s (my version of) the Variable Mass (VM) theory. Instead of Milgrom’s ad-hoc assumption $F = m a^2/a_0$ sort of a MOND mechanism rather should be derived from more foundational and generally accepted principles.

• The frequency $(1/dt)$ of an electron in an atom is proportional to mass $m \Longrightarrow$ atomic time $t$
• The frequency $(1/dT)$ of a body in an orbit is proportional to the square root of (gravitating) mass $m \Longrightarrow$ orbital time $T$

A quotient of the two frequencies immediately leads to a very fundamental theorem of the VM theory. The two clocks are synchronized here and now at $t=T=0$ such that $dt_0=dT_0$ .

$$ \frac{dT}{dt} = \frac{dT/dT_0}{dt/dt_0} = \frac{\sqrt{m_0/m}}{m_0/m} = \sqrt{m/m_0} $$

According to the Variable Mass Theory video at 1:50 Narlikar’s law is formulated as $m = a t^2$ . Within our own version of the same theory, it must be reformulated a bit more precisely:

$$ \large \frac{m}{m_0} = (1+T/A)^2 $$

with $A=$ Age and such that $m=m_0$ for $T=0$ . It follows that

$$ \frac{dT}{dt} = 1+T/A \quad \mbox{and} \quad \frac{dt}{dT} = \frac{1}{1+T/A} $$

There is a difference between orbital velocity $v_T$ as calculated with Newton and atomic velocity $v_t$ as observed with light ($r=$ distance):

$$ \vec{v_t} = \frac{d\vec{r}}{dt} = \frac{d\vec{r}}{dT}\frac{dT}{dt} = \vec{v_T}\sqrt{m/m_0} = (1+T/A)\vec{v_T} $$

The difference becomes even more pronounced with acceleration (by repeated differentiation):

$$ \vec{a}_T = \frac{d^2\vec{r}}{dT^2} = \frac{d}{dT}\left(\frac{d\vec{r}}{dt}\frac{dt}{dT}\right) = \frac{d}{dT}\left(\frac{d\vec{r}}{dt}\right)\frac{dt}{dT} + \frac{d\vec{r}}{dt}\frac{d}{dT}\left(\frac{dt}{dT}\right) = \frac{d^2\vec{r}}{dt^2}\left(\frac{dt}{dT}\right)^2 + \frac{d\vec{r}}{dt}\frac{d^2t}{dT^2} $$

where

$$ \frac{dt}{dT} = \frac{1}{1+T/A} \quad \Longrightarrow \quad \frac{d^2t}{dT^2} = -\frac{1/A}{(1+T/A)^2} $$

and so

$$ \vec{a}_T = \frac{d^2\vec{r}}{dt^2}\left(\frac{1}{1+T/A}\right)^2 - \frac{d\vec{r}}{dt}\frac{1/A}{(1+T/A)^2} = \frac{\vec{a}_t - \vec{v}_t/A}{(1+T/A)^2} $$

It is thus seen that even for $T=0$ - that is here and now - there is an anomalous component of the acceleration, which makes a difference for the two timeframes (orbital vs. atomic):

$$ \vec{a}_T = \vec{a}_t - \vec{v}_t/A \quad \mbox{or} \quad \vec{a}_t = \vec{a}_T + \vec{v}_T/A $$

Galaxy rotation curves

Contrary to what one would expect, Mordegan’s acceleration in MOND is analogous to velocity in the VM theory. It is assumed that (elementary rest) mass is varying across the galaxy, in such a way that new mass is created in the center and becomes more aged when spiralling in outward direction $r$ . As a first attempt to mimick the true Galaxy rotation curve, the following hypothesis has been tried: (elementary rest) mass is proportional to the distance from the center of the galaxy. Formally: $m \sim r$ , simply a linear relationship to begin with. Let $R=$ radius of the galaxy, then

$$ |\vec{v}_t| = |\vec{v}_T|\sqrt{m/m_0} = |\vec{v}_T|\sqrt{r/R} \quad \Longrightarrow \quad v_t = \sqrt{r/R}.v_T $$

According to Newtonian mechanics, for the circular orbit of a star around a gravitating body with mass $M$ :

$$ \frac{GMm}{r^2} = m\frac{v_T^2}{r} \quad \Longrightarrow \quad v_T = \sqrt{GM/r} \quad \Longrightarrow \quad v_t = \sqrt{r/R}.\sqrt{GM/r} = \sqrt{GM/R} $$

which is indeed a flat rotation curve, as observed in the atomic time frame with our telescopes. Without MOND, without Dark Matter.

Appendix

The Variable Mass Theory has originally been devised for the purpose to have an explanation for the cosmic redshift. With $\lambda=$ wavelength of light, the redshift $z$ is defined as

$$ z = \frac{\lambda - \lambda_0}{\lambda_0} \quad \Longrightarrow \quad 1+z = \frac{\lambda}{\lambda_0} = \frac{c.dt_0}{c.dt} = \frac{m}{m_0} = (1+T/A)^2 $$

With help of the previous, relationships between orbital time $T$ and atomic time $t$ are derived.

$$ \frac{dt}{dT} = \frac{1}{1+T/A} \quad \Longrightarrow \quad t = \int\frac{dT}{1+T/A} = A.\ln(1+T/A) \quad \Longrightarrow \quad 1+T/A = e^{t/A} $$

Combining with the redshift gives for the cosmic distance $D$

$$ D = c.t = c.A.\ln(1+T/A) = c(A/2)\ln([1+T/A]^2) = c(A/2)\ln(1+z) $$

A well known formula is thus re-established.

$$ \large D = c/H.\ln(1+z) $$

Provided that the Hubble parameter is not one divided by Age, but twice that value: $H=2/A$ (Narlikar). At last, the Variable Mass can be expressed in both orbital and atomic time with the Hubble:

$$ \frac{m}{m_0} = \left(1+\frac{1}{2}H.T\right)^2 = \large e^{H.t} $$

The frequency of an electron in an atom is proportional to mass m => atomic time t

Based on what?

A quotient of the two frequencies immediately leads to a very fundamental theorem of the VM theory.

What is the basis for making this quotient?

new mass is created in the center and becomes more aged when spiralling in outward direction r

According to what?

I’m not convinced your theory is offering any clarity on the known v^4 ~ M galactic relation.

The improvement to MOND, in my opinion, should connect MOND’s galactic acceleration contribution to local stellar, planetary acceleration contributions.

For example, the ISS has an instant acceleration [~ 9 m/s^2 in the dir of the Earth] + [~ 6 * 10^-3 m/s^2 in the dir of the Sun] + [~ 2 * 10^-10 m/s^2 in the dir of galactic center], a vector sum. (The ~ 2 * 10^-10 m/s^2 is > a0, so it’s not an exemplar of apply-MOND-when-g<a0, but the point is the total acceleration of an object orbiting a planet is a sum of components which weren’t all calculated the same way. That needs justification.)

The improvement to MOND should output the total acceleration of a particle given a 3D point cloud of a galaxy (a list of points with their mass, position, velocity, and for test, acceleration).

I’m not convinced your theory is offering any clarity on the known v^4 ~ M galactic relation.

See MOND ⊆ VMT :

$$ \left(v_t^2\right)^2\mbox{ (VMT)} = v^4\mbox{ (MOND)} \quad \Longrightarrow \quad \left(\frac{GM}{R}\right)^2 = GM\mbox{ }a_0 = v^4\mbox{ (MOND)} $$

As for the rest of your questions, I have made adjustments in place.

You referenced Rydberg’s constant… how does that prove “The frequency of an electron in an atom is proportional to mass m” ?

A quotient of the two frequencies immediately leads to a very fundamental theorem of the VM theory.

Why make this quotient?

new mass is created in the center and becomes more aged when spiralling in outward direction r

What is the evidence?

An improvement to MOND will produce the total acceleration on a particle.

Here is one attempt, which is a program that runs on every particle.

const r_cutoff = 10^15 meters    // ~ 10,000 AU, this is a guess

function calc_accel_for_particle() {
    a_classic = 0
    a_far = 0

    for each mass:               // each mass in the 3D point cloud
        a_classic += Gm/r^2

    for each mass farther than r_cutoff:
        a_far += Gm/r^2
    a_far = sqrt(a_far * c^2/87Gly)

    a_total = a_classic + a_far

    return a_total
}

but it is not elegant as it doesn’t explain why there’s an r_cutoff, why it has a certain value and can be no other value, and why there’s a sum of components which weren’t all calculated the same way.

The r_cutoff, beyond which a separate acceleration program applies, is similar to the current understanding of the nuclear force, which has an r_cutoff of ~ 2.5 * 10^-15 m, within which a separate force program applies.

The total charge-related force on a proton considering all particles in a 3D point cloud is something like this:

const r_cutoff = 2.5 * 10^-15 meters    // https://en.wikipedia.org/wiki/Nuclear_force

function calc_force_on_proton() {
    f_near = 0
    f_classic = 0

    f_near = specialfx(all particles within r_cutoff)    // don't know the special function, but f_near is attractive

    for each particle:
        f_classic += k(q_proton)(q_particle)/r^2

    f_total = f_near + f_classic

    return f_total
}

Does anyone have a better way to calculate the total charge-related force on one proton given a 3D point cloud?

Also, an explanation for [why Modified Coulombian (or Coulombic) Dynamics kicks in within ~ 2.5 * 10^-15 m] might open a door to [why MOND-redefined-for-total-acceleration-calculation kicks in beyond ~ 10^15 m].

Our Galaxy project and the Continuing story of it has resulted in the following (Delphi) Pascal code.

{
This software has been designed and it is
CopyLefted by Han de Bruijn:

                          (===)
                         @-O^O-@
                          #/_\#
                           ###

UNIFIED ALTERNATIVE COSMOLOGY GALAXY PROJECT
============================================
}

Rest deleted, for the sake of saving bandwidth.

accepting [MOND explains wide binaries] requires [MOND accelerations are addable], which allows a procedure to calculate total acceleration which leads to a false value. Therefore [MOND explains wide binaries] has an issue. Does this make sense?

@sahil5d your argument makes sense for [MOND as modified inertia] = [ $\vec{F} = m \vec{a} \mu(a/a_0)$ ] ! Since the “interpolating” function $\mu(a/a_0)$ is non linear, the order of the summation is important.

If a star $i$ produces an acceleration $a_i$ on star $A$, it is not clear how to do the summation to determine if star $A$ is in the MOND regime or not.

In other words, the force on star A obtained by adding the individual MOND contribution of each other star $i$ (including star B) in the galaxy

$$ \vec{F}_A = m_A \sum_i \vec{a_i} \mu \left( \frac{a_i}{a_0} \right), \quad \mbox{where} \quad a_i=|\vec{a}_i|, $$

is not the same as the force obtained by taking the vector sum on the entire galaxy as a unit

$$ \vec{F’}_A = m_A \left[ \sum_i \vec{a_i} \right] \ \mu \left( \frac{ \left| \sum_j \vec{a}_j \right|}{a_0} \right). $$

I haven’t read the “Wide Binary paper” in details, do they add star B separately from the galaxy?

If so, this would mean

$$ \vec{F’’}_A = m_A \left[ \sum_i \vec{a_i} \right] \ \mu \left( \frac{ \left| \sum_j \vec{a}_j \right|}{a_0} \right) + m_A \vec{a_B} \mu \left( \frac{a_B}{a_0} \right) \quad \mbox{ for} \quad i \ne B $$

which would be a serious issue.

For [MOND as modified gravity] they use the total potential, so that would be like calculating $\vec{F’}_A$…

P.S. This is the arbitrary part of MOND that I don’t like, Milgrom et al. are just trying different equations that don’t make physical sense, so they are free to “move the goal posts” until they find an equation that works. For exemple, why not calculate

$$ \vec{F’‘’}_A = m_A \left[ \sum_i \vec{a_i} \right] \ \mu \left( \frac{ \sum_j \left| \vec{a}_j \right|}{a_0} \right). $$

which would give another value!

The frequency differential is created by the different powers of infinity of the Photons that make up the field, product of the fact that said field is a FLAT SPHERE – this is another side effect, a unique and exclusive product of the physical process of Gravity.

Every celestial body with gravity (except naked stars or misnamed “black holes”) and their respective finite, determined and countable gravitational fields are flat spheres by definition. The issue lies in the very definition of a straight plane – any one, whose radius of curvature at any point on its surface is equal to infinity. This is what happens with our planet – the radius of curvature at any point of its spherical surface is equal to infinity, and therefore it is a «flat sphere» or if you prefer, a «straight plane curved on itself». Look at my work: «The Gravitational Paradox and the Proposed Experiment to Demonstrate Gravitational Distortion of “Spacetime”» In English, Russian and Spanish versions, revised and expanded. 15 pages. 2 drawings. https://vixra.org/abs/2202.0042