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CHAPTER 5: A SEMI-CLASSICAL CALCULATION REGARDING THE MASS-DENSITY OF SO CALLED “NEUTRON STARs”

CHAPTER 5:   A SEMI-CLASSICAL CALCULATION REGARDING THE MASS-DENSITY OF SO CALLED “NEUTRON STARs”  by  MARK CREEK-WATER DORAZIO, ApE (amateur physics-enthusiast),  MARK.CREEKWATER@gmail.com

“Accepting the universe as rational … we should reject such irrational concepts as singularities with infinite temperatures and densities in discussing it … if we can avoid such unphysical concepts rationally, we should do so even if we must depart from current dogma and the presently accepted models” —–Dr. LLOYD MOTZ, astrophysicist, Columbia University [Ref.#29] …

SUMMARY OF THE ESSAY

ZWICKY and BAADE in 1933, soon after the discovery of neutrons, predicted the existence of “NEUTRON STARs” [Ref.#14] … KIP THORNE [Ref.#13] calls their paper “one of the most prescient” in all of 20th century physics, because it correctly predicted the existence of very dense, rapidly rotating, objects, which were not observed until almost 35 years later …

Based on the work of STERNGLASS [Ref.#1 + Ref.#1a] and SIMHONY [Ref.#2 + Ref.#2a] one can propose that there might be a MAXIMUM MASS-DENSITY for a collapsed star, and for collapsed stars in general, which might prevent it/them from collapsing down to a zero-volume “SINGULARITY” which would produce a so called “black hole” …

Specifically, for reasons which I explain below, one can propose that the mass-density of “neutron stars” might be nearer to 5 x 10^(15) grams/cc than to the commonly accepted numeric value of approx. 3 x 10^14 grams/cc …

Using easy maths, (high school algebra + geometry), one can calculate that one might expect that a “neutron star” [i.e., a SUPERNOVA REMNANT] whose mass-density [M-D] is approx. 5 x 10^(15) grams/cc would have a mass of approx. 1.9x that of our sun, and a radius of approx. 5.6 km … this helps explain why most “neutron stars” have masses between 1.4 x that of our sun and 1.9 x that of our sun, until now a mystery [p.192, Ref.#13] …

{NOTE: IN THIS ESSAY, THE WORDs “NEUTRON STAR” AND “BLACK HOLE” APPEAR IN QUOTATON MARKs, DUE TO THE AUTHOR’s SINCERE BELIEF THAT THERE MIGHT BE SERIOUS ERRORs INVOLVED IN SOME OF THE COMMON IDEAs + ASSUMPTIONs REGARDING THESE OBJECTs} …

TEXT OF THE ESSAY

Ironicly, and in spite of what some of us have been taught to believe, re the nature of “black holes” and “neutron stars”, it seems like the average “neutron star” might be MORE dense than the average “black hole” [!!] —– if, in fact, there is a maximum mass-density for collapsed stars in our universe …

When a massive star collapses and goes supernova, there is usually a large explosion, and much of the star’s matter is lost, so its mass is greatly reduced … what remains, (a supernova “remnant”), is also called a “neutron star” or a “pulsar” …
During the past 50 years, researchers have determined that most “neutron stars” are of a mass between 1.4 x and 1.9 x that of our sun [Ref.#13];  i.e., they’re very dense, but not very massive, given that some stars are > 100 x as massive as our sun …

ONE CAN RECKON THAT standard textbook descriptions of “black holes” might be incorrect, because they’re based on a collapse to a “singularity” of radius approaching zero:  as Dr. Lloyd Motz, a colleague of Sternglass, observes:  “Accepting the universe as rational … we should reject such irrational concepts as singularities with infinite temperatures and densities in discussing it … if we can avoid such unphysical concepts rationally, we should do so even if we must depart from current dogma and the presently accepted models” [Ref.#29] …

I.e., one can reckon that, long before a “black hole” shrinks down to a “singularity”, there might be a natural, inherent, “MINIMUM APPROACH DISTANCE” [Sternglass’s words, p.203, Ref.#1] for the bits of matter in the collapsed star, which gives to it a MAX M-D of approx. 5 x 10^(15) grams/cc …

Sternglass says that “black holes” do exist in his model of our universe, but only up to a mass-density comparable to that of ordinary protons + neutrons;  i.e., approx. 3.0 x 10^14 grams/cc [p.206, Ref.#1] … Alternatively, I propose a MAX M-D of approximately 17 times that, (i.e., approx. 5 x 10^15 grams/cc) … This proposal is based on my intense study of Sternglass’s model, “The Electron-Positron Pair Model of Matter” [Refs. #1 + #1a], and that of Simhony, “The Electron-Positron Lattice Model of SPACE” [Refs. #2 + #2a] …

Tho the 2 gentlemen, (ages 91 and 92 in 2014) never collaborated, their independently developed models support and affirm each other …

STERNGLASS’s MODEL .  .  .
. . . gives a believable scenario for what might have happened before the so called “BIG BANG” —– and before the formation (one wants to say “creation”) of protons + neutrons, which evidently did not exist until then …

NOTE: THO I KNOW THAT SOME SCIENTISTs SAY THAT A “BIG BANG” NEVER HAPPENED, I ALSO KNOW THAT STERNGLASS GIVEs SOME POWERFUL EVIDENCE TO SUPPORT THE IDEA THAT A “BIG BANG” REALLY DID HAPPEN …

IN “TABLE 1” [p.234, Ref.#1] STERNGLASS LISTs “Masses, Sizes, and Rotational Periods of Cosmological Systems Predicted by the Electron[-Positron] Pair Model of Matter” … All the familiar kinds of physical objects are there, from galaxies + stars + planets, down to sub-atomic entities …

If one extend this “TABLE 1” a bit farther than Sternglass did in the book, “down” into the section which he would call “STAGE 28”, then one sees that there is room for a tiny “system”, WHOSE MASS IS THAT OF AN ELECTRON, and WHOSE RADIUS IS APPROX. 4.1 x 10^(-15) cm; i.e., approx. 4.1 x 10^(-17) meter … THE MASS-DENSITY OF SUCH A TINY SYSTEM, IF ONE ASSUMEs THAT IT IS OF A TORUS-[DONUT]-SHAPE, WOULD BE APPROX. 5×10^15 grams / cc —– INSPIRING ME TO PROPOSE THIS NUMERIC VALUE AS A MAXIMUM MASS-DENSITY FOR THIS KIND OF “STUFF” IN OUR UNIVERSE …

If there is, in our universe, a maximum mass-density for a collapsed star of approx. 5 x 10^(15) grams / cc, then this might mean that a “black hole” can be no more dense than that … If so,  then,  because (according to the “Schwarzschild formula” for the radius of a “black hole”) smaller “black holes” are more dense, there must be a particular “black hole”, WHOSE MASS-DENSITY IS APPROX. 5 x 10^15 grams/cc, which would be the most dense “black hole” possible — and also the least massive;  because, as already mentioned, a smaller “black hole” would be more dense …

The maths are easy and straight-forward:  assuming that a “black hole” is sphere-shaped, and satisfies the so called “SCHWARZSCHILD CONDITION”  [(Rbh) = 2G x (Mbh) / c^2],  then one has:
(MASS-DENSITY)bh = (Mbh) / (VOL)bh = [Mbh] / [(4/3)x(pi) x (Rbh)^3] =
[Mbh] / {4.2 x [2G x (Mbh) / (c^2)]^3} = [c^6] / [4.2 x 8 x G^3 x (Mbh)^2],  
where “Mbh” is “black hole” mass, “Rbh” is “black hole” radius, “G” is Newton’s gravitational constant, and “c” is the speed of light …

Equating this (MASS-DENSITY)bh to  (5 x (10)^15 grams/cc)  implies:   (Mbh) = { [c^6] / [33.6 x G^3 x (5 x 10^15 gm/cc)] }^(1/2) … Please note that the “^(1/2)” at the end means that one calculates the square-root of the entire expression …

Using numeric values G = 6.7 x 10^(-8) cc / gram.sec.sec, and c = 3 x 10^10 cm/sec, one calculates that (Mbh) = approx. 1.9 x the mass of our sun [i.e., approx. 3.8 x 10^(33) grams], as already mentioned … But in almost every real star-collapse, this reduces to approx. 1.4 x our sun’s MASS, due to the fact that there is almost always a SUPERNOVA EXPLOSION when a massive star collapses, which blows away much of its mass, even some of the potential “remnant” mass of approx. 1.9 x that of our sun, which might remain after a less energetic explosion …

{ One can visualize a star whose initial mass is approx. 1.9 x that of our sun collapsing down to “neutron star” size, BUT NOT EXPLODING … However, because more massive stars “burn” their fuel more rapidly than less massive stars, one expects that the vast majority of supernova explosions involve stars whose initial masses were >> 1.9 x that of our sun, some > 100 x that of our sun … Such as, for example, the supernova known as SN2006gy, whose light needed > 100 million years to travel from there to here !! } …

Obviously, the more massive the star, the more violent the explosion;  so most supernova remnants are nearer to 1.4 x than to 1.9 x the mass of our sun …

IN OTHER WORDs:  WHEN A STAR COLLAPSEs, IT USUALLY EXPLODEs;  BUT IF CONDITIONs ARE JUST RIGHT, THEN IT MIGHT COLLAPSE AND NOT EXPLODE … If it doesn’t explode, then it will retain more mass, and if it produces a “neutron star”, then that “neutron star” will also [in German, “also” means “therefore”] be more massive than one produced by a star which collapses and explodes …

In this way, one realizes that a collapsed star whose mass is approx. 1.9 x that of our sun represents an object which is “on the border-line” between “neutron star” and “black hole”:  i.e., one can call it either “the most massive ‘neutron star’ possible” or “the least massive ‘black hole’ possible” …

Also in this way, one realizes that such a collapsed star (supernova remnant) might be composed of (NOT NEUTRONs, BUT) tiny objects which are smaller and more dense than neutrons …

The description above answers the open question implied in KIP THORNE’s book Black Holes and Time Warps, where he says that:
“SINCE 1967 HUNDREDS OF NEUTRON STARS HAVE BEEN OBSERVED BY ASTRONOMERS, AND THE MASSES OF SEVERAL HAVE BEEN MEASURED WITH HIGH ACCURACY … THE MEASURED MASSES OF ALL ARE CLOSE TO 1.4 SUNS; WHY, WE DO NOT KNOW” [p.192, Ref.#13]

MORE DETAILs

Recently [Ref.#15] some astronomers published results of their observations of a “neutron star” [known as  J1614-2230] whose mass they determined to be approx. 1.9 x that of our sun, evidently one of the largest masses ever observed for a “neutron star” …

Quote from Ref.#15:  “We measure a pulsar mass of (1.97 +/- 0.04) solar-masses, which is by far the highest precisely measured neutron star mass determined to date” …

PLEASE NOTE THAT THIS OBSERVATIONAL RESULT SUPPORTs THE PROPOSAL FOR A MAXIMUM MASS-DENSITY OF APPROX. 5 x 10^15 gm/cc FOR “BLACK HOLEs” AND/OR “NEUTRON STARs” … If the ideas and the numbers presented here are correct, then such a “neutron star”, whose initial mass before collapse was approx. 2 times that of our sun, was just the right amount so that it collapsed but then did not explode, which enabled it to retain all of its initial mass …

Please also note the following, from Dr. Fulvio Melia at the University of Arizona in Tucson:  “Interestingly, [assuming] that the emitting surface is spherical, one derives a photospheric radius of only ~6.4 +/- 1.4 km … small for a neutron star” [p.238, Ref.#16] …

On the contrary, based on the ideas and the numbers presented here, that seems to be just about the right size for the radius of an average “neutron star” … In the case of a collapsed star whose mass is 1.9 x that of our sun, one calculates its radius as:
(Rbh) = [2G x (Mbh)] / (c^2) = 2 x [6.7 x 10^(-8) cc / gram x sec^2] x [3.8 x 10^33 grams] / [9 x 10^20 cm^2/sec^2]  = 5.6 x 10^5 cm = 5.6 km  … Please note that this is within the range (above) of “~6.4 +/- 1.4 km” …

Evidently, this researcher has found some evidence to support the idea that the radius of a “neutron star” which he studied might be smaller than the 10 km size which most textbooks give …

The fact that most textbooks give approx. 10 km as the radius of an average “neutron star” is obviously based on the assumption, perhaps incorrect, that the mass-density of a “neutron star” should be approx. that of a neutron;  i.e., approx. 3 x 10^14 grams / cc … If it’s more dense, then it’s also smaller …

Please note that a recent conversation which I pursued on a popular physics internet-site produced no compelling evidence that astronomers have ever made any DIRECT measurement of the radius of a supernova remnant, as, evidently, there are none close enough to us for them to be able to do so …

One suspects that the 10 km radius which the books give might be based on incorrect theory, instead of on accurate observations and measurements …

PHYSICAL EXPLANATIONs ??

How might one offer a physical explanation for the proposal that there is a MAX M-D for the “stuff” in our universe, which prevents the formation of a “small” “black-hole” — i.e., one whose mass is less-than 1.4 x that of our sun ??
IE: WHAT PHYSICAL MECHANISM PREVENTs THE TOTAL COLLAPSE WHICH SOME OF US HAVE BEEN TAUGHT TO BELIEVE IN ??

In Sternglass’s model, neutrons and protons are NOT composed of “quarks” — which have never been observed in a physics lab [Ref.#17, pp.323-324] … instead, they’re composed of SPEEDY ELECTRONs + SPEEDY POSITRONs — which are DEFINITELY KNOWN TO EXIST !!

In fact, the schematic diagram on p.250, Ref.#1 clearly shows that there are, in Sternglass’s model, three [3] parts to each proton or neutron: LEFT SIDE + CENTER + RIGHT SIDE, analogous to the three “quarks” which are supposed to compose each proton or neutron, according to the Standard model … Sternglass has no problem with quark-theory — and mentions it in his book, several times:  he just simply shows that “quarks” are composed of smaller “particles”:  SPEEDY ELECTRONs + SPEEDY POSITRONs …

One suspects that, when a massive star collapses, not only do most of its ordinary protons + electrons get CRUSHED TOGETHER, which forms neutrons, but that these neutrons then BREAK APART, somewhere between a mass-density of (3 x 10^14 gm/cc) and (5 x 10^15 gm/cc), into the SPEEDY ELECTRONs + SPEEDY POSITRONs which compose them [p.250, Ref.#1]

{ One can call this stuff “degenerated neutrons” and, as already mentioned, calculate that it is composed of objects which are smaller and more dense than neutrons … One can even propose to call this kind of SN-remnant a “quark star”, as some PhD-holders have done [ http://physicsworld.com/cws/article/news/2010/jan/15/calculations-point-to-massive-quark-stars ], and this would make sense, according to quark-theory, despite the fact that, as already mentioned many times throughout this series of essays, “quarks” have never been observed in a physics lab [pp.322-324, Ref. #17] } … 

MEANWHILE, THERE ARE LOTs OF NEUTRINOs TRAPED INSIDE THE COLLAPSING STAR:  one suspects (based on one’s reading) that it’s mainly these NEUTRINOs — (at the immense mass-density of approx. 5 x 10^15 grams/cc)— which prevent further collapse, and, in most cases, cause the star to REBOUND ===>>!!BOING!!<<=== creating A SUPERNOVA EXPLOSION …

After the explosion, there is a very small, very dense, and very rapidly rotating supernova “remnant” left behind:  one can visualize that SPEEDY ELECTRONs + SPEEDY POSITRONs have emerged, IN EQUAL NUMBERs, from the crushed and broken neutrons, and formed ELECTRON-POSITRON PAIRs, also called “DIPOLEs”:  one can visualize these tiny objects, many many tons of them, each with the mass of a single electron and a radius of approx. 4.1 x 10^(-15) cm [4.1 x 10^(-17) meter], as composing a so called “neutron-star” …

As already mentioned, Dr.Sternglass’s “TABLE 1” [p.234, Ref.#1] predicts the existence of these “objects which are smaller and more dense than neutrons” … assuming that they are of a TORUS-[DONUT]-SHAPE, their mass-density would be approx. 5 x 10^(15) grams/cc …

CONCLUSION:  Perhaps, what we have (until now) called “neutron stars” might (in fact) be composed of these “objects which are smaller and more dense than neutrons” … Perhaps, for now, one might want to refer to “neutron stars” as just simply “supernova remnants” …

A TESTABLE PREDICTION:  Based on the ideas and the numbers presented in this essay, one can PREDICT that, when astronomers are able to make accurate DIRECT measurements of supernova remnants, then they will agree that the RADIUS of a typical supernova remnant is nearer to 6 km than to the current accepted value of approximately 10 km …..

SINCERELY, MARK “TRUTH-LOVER” CREEK-WATER DORAZIO, ApE (amateur-physics-enthusiast),

BERKELEY, CA, USA, 20-DECEMBER-2013;  E-MAIL: MARK.CREEKWATER@GMAIL.COM

$$$$$$$$$$$$$$ << END OF CHAPTER 5 >> $$$$$$$$$$$$$$

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9 comments on “CHAPTER 5: A SEMI-CLASSICAL CALCULATION REGARDING THE MASS-DENSITY OF SO CALLED “NEUTRON STARs”

  1. marktruthlover
    August 26, 2014

    EXCELLENT ESSAY !!

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