Essay talk:Gravitation demystified

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Calculation of Hubble's constant

JJ, please show your calculations for Hubble's constant. You say I calculated it from plain Newtonian math. I am intrigued (((Zack Martin)))^™ 08:18, 21 July 2011 (UTC)

Hi Mar, For some reason I didn't have access to the internet almost whole last week (I'm in Poland now) but now I'm writting from my school and luckily it has access to the internet.

I'll write all steps (less than a dozen) and you write me if you understand them. The derivation is on my university physics server that I keep sending it from to various scientific journals who regret that they can't publish it for not yet disclosed reasons. Neither they disclosed yet why they don't send this paper through a peer review process.

I'll type the calculations manually, one step at a time, numbering steps, so you can write me if you understand all steps and if not then why. It has an advantage that I'll have it in wiki form too (so far I have it in TEX, PS, PDF and HTM(L) since various jornals want it in a different form and I don't have a program translating it to WIKI (I might write it when I have more time). JimJast (talk) 13:48, 30 July 2011 (UTC)

Step 1. Assumptions

The basic assumption is that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few, it makes no diff). Average density of this dust is $\rho$ (and this is impportant and that's why number of galaxies corresponding to one dust particle is not important). Additionally we assume that $\pi$ is what it usually is, $c$ is speed of light, $G$ is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden tricks.

Now light starts radiating from some arbitrary "point zero" and photons start interacting with galaxies through "dynamical friction of photons" (the gravitational effect known in astronomy as "dynamical friction" but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius $r$ around "point zero" is $E_{d}(r)$. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

After photons of energy $E_{o}$ are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate $r=0$ in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

$F_{galaxy}(r)=(G/c^{2})[E_{o}-E_{d}(r)]m_{galaxy}/r^{2},$

and

$F_{galaxy}(r)=-dE_{galaxy}(r)/dr$

where $E_{galaxy}(r)$ is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance $r$ from "point zero".

N.B. Usually astrophysicists neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not exact but they think that no harm is done by small negligence of exactness of math. Apparently they are wrong as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed.

Explanations of the above equations:

The first one comes from the Newtonian force being $F=GMm/r^{2}$ and $M$, the source of gravitational force being replaced by $M=E/c^{2}$ according to Einstein's physics. $E$ in this equation is diff of original mass of "dust" causing the "Newtonian attraction" adjusted by small $E_{d}(r)$ causing a "repulsion" (acting in opposite direction than $M$). The rest is straight forward, but if not then ask.

Step 2: Integrating the mass of galaxies

... of spherical shell of radius $r$ of galaxies around "point zero" and thickness $dr$ gives number

$m_{shell}=4\pi \rho r^{2}dr$,

where $m_{shell}$ is the mass of whole thin (of thickness $dr$) shell of galaxies of radius $r$ and

$F_{shell}=(G/c^{2})[E_{o}-E_{d}(r)m_{shell}/r^{2}$

Step 3. Calculating sum of all forcess acting on the shell

Substituting number from step 2 for the mass of galaxy resulting in

$F_{shell}(r)=(4\pi G\rho /c^{2})[E_{o}-E_{d}(r)]dr$.

and

$F_{shell}(r)=-dE_{shell}(r)/dr$.

and so

$-dE_{shell}(r)/dr=(4\pi G\rho /c^{2})[E_{o}-E_{d}(r)]dr$.

Step 4. Integrating both sides of above equation

$-dE_{d}(r)/dr=(4\pi G\rho /c^{2})\int [E_{o}-E_{d}(r)]dr$

... over all spherical shells between "point zero" and $r$ to get total energy of "dust" absorbed from photons, and then differentiating both sides with respect to $r$ to get rid of integral on the right side of this equation, we get finally the starting $E_{d}(r)$ where subscript $d$ now, as before, means "volume of universe of radius $r$ around point zero"

$-d^{2}E_{d}(r)/dr^{2}=(4\pi G\rho /c^{2})[E_{o}-E_{d}(r)]$.

Step 5: Setting differential equation controlling the redshift

Substituting $E_{d}(r)=E_{o}-E(r)$ where $E(r)$ is energy of photons at distance $r$ from their source and $1/R_{E}^{2}=4\pi G\rho /c^{2}$, number called in cosmology "curvature of space of Einstein's universe" (or $R_{E}=$"Einstein's radius of universe"), we get

$d^{2}E(r)/dr^{2}=E(r)/R_{E}^{2}$

Step 6: Solving the above equation

with initial conditions $E(r=0)=E_{o}$

and $(dE/dr)(r=0)=-E_{o}/R_{E}$ meanig selecting a solution that makes physicsl sense) one gets solution

$E/E_{o}=exp(-r/R_{E})$

Step 7: Slowing of proper time in deep space

Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

$d\tau /dt=exp(-r/R_{E})$,

where $d\tau$ is proper time in deep space and $t$ is coordinate time at observer. The effect might be called "Hubble Timr Dilation" (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the essential relativity of time of Einsteinian theory.

Excelent agreement of the shown in step 11 acceleration of apparent expansion of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

Step 8. Flatness of spacetime

Differentiating the above equation at $r=0$ we get the relation between HTD in deep space $(d^{2}\tau /dtdr)^{2}$ and the curvature of space of Einstein's universe $(1/R_{E})^{2}$ as

$(d^{2}\tau /dtdr)^{2}-(1/R_{E})^{2}=0$

It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively $H_{\mu \nu }$ or Hubble Tensor (HT) such that $H_{\mu \nu }+R_{\mu \nu }=0$, where $R_{\mu \nu }$ is as before the (spatial) part of Ricci tensor, and $H_{\mu \nu }$ is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of $T_{\mu \nu }$ and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress energy tensor as asserted by Feynman in 2nd volume of "Feynman lectures on physics".

So all the pieces of puzzle seem to fit the ancient "principle of conservation of energy". They oppose the speculations of authors of 1973 "Gravitation" by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation and Carl Sagan.

But look at the further steps, even more interesting.

Step 9. Hubble redshift

It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

$Z=(\lambda -\lambda _{o})/\lambda _{0}=(E_{o}-E)/E=exp(r/R_{E})-1$,

where $\lambda _{o}$ and $\lambda$ are respectedly the "expected" wave (without the redshift) and the received one.

Step 10. The same thing in form of Hubble "constant"

Such redshift simulates the expansion of space, with Hubble constsnt of this apparent expansion at $r=0$ equal

$H_{o}=c/R_{E}$

It is observed as about $H_{o}=$70km/s/Mpc which implies that the radius of curvature of space of Einstein's model universe, $R_{E}$ is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of $H_{o}$ implies the density of our universe about $6\times 10^{-27}kg/m^{3}$, which is about what is observed.

Step 11. Apparent accelerating expansion of space

After expanding Hubble "constant" $H(r/c)=H(t)$ into Taylor series around $t=0$ acceleration of this apparent expansion is approximately equal

$dH(t)/dt=-H_{o}^{2}/2$.

the above velue agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

So the "accelerating expansion of our universe" blamed on mysteious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the "biggest blunder of Einstein's life") which can be shown not to exist at all. I happen to eliminate it from Einstein's field equation in rather straight forward manner more than 25 years ago. Though couldn't show it Einstein for his approval since he was aready dead.

It might have been also discovered by Mileva Marić Einstein, who seemed much smarter than Albert and who might have kept this from Albert as a secret because of their problems with their mariage. She was probably too angry to tell him how to get rid of this "biggest bluder of his life" but in fact only a small mistake on Albert's part which shouldn't be there in the first place if he treated the relativity of time more seriously.

But Mar, before asking me about "Einstein's cosmological constant" and my guesses about Einsteins' marital problems tell me whether you accept my high school derivation of Hubble "constant" and if not then why. I'd like to present it to CP readers and if you spot a problem, I either have to fix it before that or if I can't fix it then to reject the whole idea and convert to your religion that contradicts Einsteins' cylindrical universe. So I'm waiting for your results. BTW, I like the symbol you use with your name. Is it a religious symbol? JimJast (talk) 20:19, 28 July 2011 (UTC)

[A month later] Maratrean, Are you there? My derivation put you to sleep? It's done. Wake up and comment, please. JimJast (talk) 17:50, 28 August 2011 (UTC)

Comments please

Now, when I repeated all the derivation of Hubble redshift (HR) from my file 160.htm that I used to quote a lot but lately lost the access to (the university physics server, http://www.fuw.edu.pl/~wast/, for unexplained yet reasons) I'd like to hear some comments form you guys (and ladies as well, especially the ladies for their better thinking abilities, because of connection between both halves of your brains, that we guys miss, to make us quicker hunters and fighters but unfortunately much slower thinkers than you ladies :-( See Zofia Kowalewska, Emmy Noether, Mileva Marić. JimJast (talk) 13:49, 30 July 2011 (UTC)

Since I got blocked in conservapedia as well I have a day off from my involement in improvements of their gravitation pages and may in the meantime place here a link to this page that I got blocked out from by my university: JJ 160. And when I'm already using this forced vacation I may as well place here a link to Feynman rant complete with his chracterisation of relativists.

You're not blocked on Conservapedia. It looks like Karajou blocked you by accident and then fixed it. So, you can go back to working at CP instead. --MarkGall (talk) 18:56, 28 August 2011 (UTC)

Thanks Mark :) however ...

I just checked and I'm still blocked. Probably have to wait a little longer. Luckily I'm a patient guy. While waiting I copied the blocking text that reads:

You do not have permission to edit this page, for the following reason:

Your IP address has been automatically blocked because it was used by another user, who was blocked by Karajou. The reason given is this:

   Autoblocked because your IP address has been recently used by "JimJast". 

The reason given for JimJast's block is: "Removing content from pages"

   Start of block: 10:33, 28 August 2011
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   Intended blockee: 194.187.54.194 

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Note that you may not use the "e-mail this user" feature unless you have a valid e-mail address registered in your user preferences and you have not been blocked from using it.

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How am I to contact him or one of the other administrators when I'm blocked? On the other hand he may be one of relativists described by Feynman that I just placed a link to. And he might get angry at me. Lucky that I can kill the time chatting with you. So since I lost contact with CP could you tell me if and how could I use #REDIRECT if I needed to rename something? Still blocked in CP and getting sleepy. I'll check next weekend. JimJast (talk) 22:09, 28 August 2011 (UTC)

Essay cite

Hi Jim, we used to edit things on Wikipedia years ago before it became the wretched troll hive it is now. Love your work! Is it okay if I cite this essay (particularly the bit about using a different tensor to derive H₀ as a time dilation effect) in a talk I'm doing on "alternative" cosmological models? - Jon

Mileva Marić

Jim: You write:

Starting from rev 2.0 in June 2011, I've realised that relativity might have been discovered also by Mileva Marić (1875-1948) Albert Einstein's (1879-1955) first wife and so the refs to many things in this rev have been changed from singular to plural as in "Einsteins' theory" and "Einsteins' universe" though his blunders were kept in singular, as Einstein's "cosmological constant".

You provide no references for your suggestion/contentions about Mileva Marić, either here, or later in the article (see below). Historians of physics who has examined the contentions about Marić's alleged involvement with Einstein's achievements have found no evidence of substantive contributions to his scientific work, e.g., John Stachel. Einstein from B to Z (2002), pp. 31-38; 39-55: philoscience.unibe.ch Alberto A. Martinez. Science Secrets: The Truth About Darwin's Finches, Einstein's Wife, and Other Myths (2011), pp. 193-205; "Handling evidence in history: the case of Einstein’s Wife." School Science Review', 86 (316), March 2005, pp. 49–56: [1]

In 1905 Einsteins discovered relativity that made possible to discover also the physical theory of gravitation. They partly developed it between 1911 and 1915…

There is no evidence of any such collaboration.

…Mileva Marić, whom this author considers the principal discoverer of general relativity who most likely proposed the equation Rμν = 8πTμν considering mathematical skills of her husband.

Leaving aside that there is zero evidence for Marić having any ideas about general relativity, there have been misconceptions about Einstein's mathematical abilities in the writings of those claiming Marić's involvement in his work. His abilities in "conventional" mathematics were considerable. In the "Expert Opinion" on his Ph.D. thesis submitted to Zurich University in 1905, the professor of physics Alfred Kleiner wrote: "The arguments and calculations to be carried out are among the most difficult ones in hydrodynamics, and only a person possessing perspicacity and training in the handling of mathematical and physical problems could dare to tackle them." The opinion of Professor of Mathematics Heinrich Burkardt was sought, and he reported that he found Einstein’s calculations "correct without exception, and the manner of treatment demonstrates a thorough command of the mathematical methods involved" (emphasis in original). (A. E. Collected Papers, Vol. 5, doc. 31.) (Not being a pure mathematician, in 1912 Einstein had to seek the assistance of his mathematician friend Marcel Grossman for the more advanced pure mathematics he required for general relativity.)

It is ironic that the claim is made that Einstein was a poor mathematician as evidence for Marić's involvement given that she failed the Zurich Polytechnic (ETH) teaching diploma examination in 1900 primarily because of her very poor grade in the mathematics component (theory of functions), 2.5 on a scale 1-6. (A. E. Collected Papers, vol. 1, doc. 67.)

For a rebuttal of the claims about Einstein's mathematical abilities, see my own essay "Who did Einstein’s Mathematics?: A Response to Troemel-Ploetz". [2]

For a general rebuttal of the contentions about Marić's role, see "Mileva Marić: Einstein's Wife." [3]

See also: V. Alexander Stefan (2005), "Regarding, Inter Alia, Albert Einstein and Mileva Marich Einstein" [4]

I should add that I have tracked down all the sources for the claims about Marić's alleged contributions and found them wanting in historical credence. Esterson (talk) 14:19, 24 September 2011 (UTC)