markcreekwater

I WRITE ESSAYs

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

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

by  Mark Creek-water Dorazio,  amateur physics enthusiast,  email: MARK.CREEKWATER@gmail.com

PROLOG:   “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 (1909 – 2004), astronomer + astrophysicist, Columbia University.

 

SUMMARY [i.e., “abstract”] OF THE ESSAY

Zwicky and Baade, in 1933, soon after the discovery of neutrons, predicted the existence of “NEUTRON STARS” [Ref.#1] … KIP THORNE [Ref.#2] 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 astronomers did not observe until almost 35 years later …

Based on the work of STERNGLASS [Ref.#3 + Ref.#4] and SIMHONY [Ref.#5 + Ref.#6] 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 in the text, 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 3 x 10^14 gm/cc … Note: a “cc” is a cubic centimeter …
Using easy maths, 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. 1.9 x 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.#2] …

{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 SIGNIFICANT ERRORs INVOLVED IN SOME OF THE COMMON IDEAS + ASSUMPTIONS REGARDING THESE OBJECTS} …

 

TEXT OF THE ESSAY

Part 1:  INTRODUCTION

Ironically, 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 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” …

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;  i.e., they’re very dense, but not very massive, given that many stars are > 100 x the mass of 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 … In other words, one can reckon that, long before an object shrinks down to a “singularity”, there might be a natural, inherent, “MINIMUM APPROACH DISTANCE” [Sternglass’s words, p.203, Ref.#3] 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 …

The quote in the PROLOG, above, is from Dr. Lloyd Motz, a colleague of Sternglass …
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 x 10^14 grams/cc [p.206, Ref.#3] … Alternatively, based on Sternglass’s model, “The Electron-Positron Pair Model of Matter” [Refs. #3 + #4], and that of Simhony, “The Electron-Positron Lattice Model of Space” [Refs. #5 + #6], one can propose a MAX M-D of approximately 17 x that, (i.e., approx. 5 x 10^15 grams/cc) …

Tho the 2 gentlemen, (AGEs 91 and 92 in 2014) never collaborated, but worked independently of each other, the two models which they developed support and affirm each other …

Part 2:  STERNGLASS’s MODEL

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 HAPPEN’D, I ALSO KNOW THAT STERNGLASS GIVEs SOME POWERFUL EVIDENCE TO SUPPORT THE IDEA THAT A “BIG BANG” REALLY DID HAPPEN …

In his “Table 1” [p.234, Ref.#3] 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 extends 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 x 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 fact a maximum mass-density of approx. 5 x 10^(15) grams / cc for objects in our universe, then this means that a “black hole” can be no more dense than that … If so,  then,  because (according to Schwarzschild’s formula for the radius of a “black hole”) smaller and less massive “black-holes” are more dense, there must be a particular “black hole”, whose M-D is approx. 5 x 10^15 grams, which would be the most dense “black hole” possible — and also the smallest and least massive, because, as already mentioned, smaller less massive “black holes” are more dense …

Part 3:  A CALCULATION BASED ON STERNGLASS’s MODEL

The maths are easy and straight-forward:  assuming that a “black hole” is sphere-shaped, and satisfies the so-call’d “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  …

This implies that  Mbh = { [c^6 ] / [33.6 x G^3 x (mass-density)bh] }^(1/2),  where 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, c = 3 x 10^10 cm/sec, and (mass-density) = 5 x 10^(15) grams/cc, 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 massive 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 … But, 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 our sun, some > 100x our sun } …

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 MASSIVE STAR COLLAPSEs, IT USUALLY EXPLODEs;  BUT IF CONDITIONs ARE JUST RIGHT, THEN IT MIGHT COLLAPSE AND NOT EXPLODE …

In this way, one realizes that a collapsed star of mass 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” …

Alsp in this way, one realizes that such a collapsed star 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 [Ref.#1], 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.#2]

Part 4:  MORE DETAILs

Recently, [REF.#7] some astronomers published results of their observations of a “neutron star” [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.#7:  “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” … 

One suspects that, if the ideas and numbers presented here are correct, that that particular “neutron star” is one whose initial mass, before collapse, was of just the right amount so that it collapsed down to “neutron star” size, but then did not explode.

Please note that this observational result supports the proposal that there is a maximum mass-density of approximately 5 x 10^(15) grams/cc for “black holes” and/or “neutron stars” …

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.#8] …

On the contrary, based on the ideas and numbers presented in here, one can say that the above result, 6.4 +/- 1.4 km, is just about right … 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  …

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 the 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 …

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

{ 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 accurate DIRECT measurements of the radius of a supernova remnant } …

Part 5:  PHYSICAL EXPLANATION ??

Question:  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 ??  I.e.: WHAT PHYSICAL MECHANISM MIGHT PREVENT THE TOTAL COLLAPSE WHICH SOME OF US HAVE BEEN TAUGHT TO BELIEVE IN ??

Answer:  In Sternglass’s model, neutrons and protons are NOT composed of “quarks” — which have never been observed in a physics lab [Ref.#9, pp.322-324]) … Instead, the Sternglass proton is composed of SPEEDY ELECTRONS + SPEEDY POSITRONS — which are DEFINITELY KNOWN TO EXIST !!

In fact, the schematic diagram on p.250, Ref.#3 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 comprise each proton or neutron … Sternglass has no problem with quark theory — and mentions it several times in his book:  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, due to the immense mass-density which the collapse produces, into electron-positron pairs, similar to the pairs which compose neutrons under ordinary conditions [p.250, Ref.#3], but smaller and more dense …

{ 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 an object composed of this kind of stuff a “quark star”, as some PhD-holders have done [Ref.#10], and this would make sense, according to quark-theory, despite the fact that, as already mentioned, “quarks” have never been observed in a physics lab [pp.322-324, Ref. #9] } … 

Meanwhile, as the collapse continues, there are lots of neutrinos trapped inside:  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 supernova “remnant” left behind … One can visualize that equal numbers of speedy electrons + speedy positrons have emerged from the crushed and broken neutrons, and formed electron-positron pairs, also called “dipoles”:  one can visualize many many tons of these tiny objects, 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] and a mass-density of approx. 5 x 10^(15) grams/cc, as composing a so called “neutron star” …

As already mentioned, Dr. Sternglass’s “Table 1” [p.234, Ref.#3] predicts the existence of these tiny “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 …

Part 6:  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” …

Part 7:  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, amateur physics enthusiast, Berkeley, California, USA, 20-December-2013,   email: MARK.CREEKWATER@gmail.com

REFERENCEs

(1) Baade, Walter and Zwicky, Fritz; paper: “Supernovae and Cosmic Rays”, Physical Review, 15-January-1934;

(2) Thorne, Kip; book: Black Holes and Time Warps (1994);

(3) Sternglass, Ernest; book: Before the Big Bang (1997);

(4) Sternglass, Ernest; paper: “Relativistic Electron-pair Systems and the Structure of Neutral Mesons”, Physical Review, v.123 (1-JULY-1961);

(5) Simhony, Menahem; web-sites: http://www.EPOLA.ORG, http://www.EPOLA.co.uk;

(6) Simhony, Menahem; book: The Electron-Positron Lattice Space (1990);

(7) Demorest, P.B., et al; paper: “A Two-Solar-Mass Neutron Star Measured Using Shapiro Delay”, Nature, 25-October-2010,  (see quote below);

(8) Melia, Fulvio; book: High-Energy Astrophysics (2009);

(9) Kragh, Helge; book: Quantum Generations (1999);

(10)  http://physicsworld.com/cws/article/news/2010/jan/15/calculations-point-to-massive-quark-stars;

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QUOTE from Ref.#7 (above):  “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”

 

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