The Final Theory

[ThickSet]

My congratulations to all of you for this wonderful discussion. Clarity of thought is difficult enough, but clarity of communication can be treachorous given the conspiracy of the language. Please press on with this, it's such a treat seeing people working with each other, egos set aside, trying to sort issues out.

[Tom Palmer]

First, I want to thank all of you who have posted comments on my remarks. It is clear you are seekers after the truth about this wondrous universe and the laws that govern it. When we debate various competing models and mechanisms, it is always with the hope that, in this manner, we may be able to sort out the truth, wherever it lies. It is this quest which unifies us, even while we may disagree on the specifics.

 

There is one principle, however, that we should all be able to agree on. It is that none of us–including myself–should ever allow an unbreakable commitment to any one model blind us to contravening evidence.

 

Some of you have, like Mark McCutcheon, made quite a point about the unsolved questions underlying presently accepted theory. The implication is that, in “Marked” contrast (if you’ll pardon the pun), Mr. McCutcheon’s model is (allegedly) beautifully consistent, both within itself and with all known facts. And it is for that reason that he evidently feels he can confidently characterize his model as The Final Theory.

 

In contrast to this cocksure attitude, present-day physics is painfully aware of its own shortcomings and limitations, and is continually seeking better alternatives to, say, the Standard Model and the Big Bang. Due to human imperfections, there are unfortunately those who take an overly proprietary interest in particular models, but the field as a whole is still an arena wherein diverse ideas are lustily battling for supremacy on the basis of observation and experiment.

 

Some of you have chided physicists for stubbornly clinging to ideas such as the Standard Model and angrily rejecting any proposed alternatives. But there are alternatives being actively pursued. Supersymmetry goes well beyond the Standard Model, but it has yet to score a single major victory. String theory is radically different from the SM, but its claimed successes are heavily dependent on what I consider a ridiculously swollen number of degrees of freedom which can all too easily be made to yield any desired result.

 

In one of my emails to Chris Benfield (the “Professional Review” which the book’s website incorrectly cited in mistaken support of The Final Theory), I wrote the following:

 

<<I don't dispute Mark’s challenging the current paradigm - that can be a very good thing, even if it's done by an amateur with no professional standing in "the club". It's really the only way science can make major advances ("paradigm shifts"). And I can't object to the fact that his ideas may seem strange and counterintuitive - that, too, can be a very good and necessary thing.

 

What I do object to is what I perceive as arrogance and shameless self-promotion (with a touch of paranoia), coupled with a tiresome habit of shaky, simplistic "proofs" that aren't - whether they are supposed proofs of his ideas, or alleged disproofs of the prevailing view. I'm not interested in "circling the wagons" (as we say over here in the States) in order to defend orthodoxy from heresy. If another model overturns the current one, that's fine by me. But it has to be done honestly.>>

 

Please note that final sentence: “If another model overturns the current one, that's fine by me. But it has to be done honestly.” And that, as I see it, is where MMcC’s book falls flat–it does not honestly deal with its contradictions. If only the book’s contents were as beautiful as its cover.

 

Tom Palmer

[Tom Palmer]

Okay, good. Then the current model for that measurement works. That doesn't mean the model is correct though. When I read up on the Lamb Effect it mentioned 'virtual protons' so, I suspect that there is still something that is not quite understood in that model.

Bundling photons into stable configurations representing discreet colors of light where the difference between two adjacent colors might be constant or might not. In other words, 'frequencies' of light would progress in jumps between stable configurations. Assuming we actually have an accurate way of measuring those differences, perhaps we could infer something about the composition of the 'frequencies'. But see, we wouldn't look there if we are hanging on to the wave theory of light.

For openers - I think you meant to say "virtual photons" (not "protons").

 

You say that, although the measurement works, it doesn't mean the model is correct. Strictly speaking, that is true--for any model, including Mr. McCutcheon's. And, to my knowledge, he doesn't have even one solid, mathematically demonstrable success to back up his claims.

 

However, a major success like the exquisitely accurate prediction of the Lamb shift can't just be minimized and blown off as if it didn't really prove anything. In point of fact, it considerably ups the ante in favor of the model, even though that model may in time be supplanted by an even more accurate one.

 

As for the wave theory of light, its successes are considerable, Mr. McCutcheon to the contrary notwithstanding. If a competing model can duplicate (or even outperform) all of those successes, I say, more power to it.

 

But until that happens, I have a hard time imagining that adherence to the wave formulation is somehow holding back progress toward the real answers. But if it is, why doesn't The Final Theory give us even one real, unequivocal, honest-to-goodness example of a superior mathematical result based on its model?

 

By that, I mean a daring, quantifiable, truly testable, falsifiable prediction on which MMcC's model stands or falls? Einstein had the guts to do it with General Relativity when, on the basis of GR, he correctly predicted the precession of the perihelion of Mercury, the gravitational bending of starlight by the sun, and even the solar gravitational red shift. And not just qualitatively, but also quantitatively.

 

Theories typically start with purely conceptual notions, but at some point, the theorist has to dust off his old college textbooks and do the math. Until then, the model is just an insubstantial castle in the sky, however pretty and appealing it might appear. Concept provides the overall form, but mathematics provides the substance.

 

McCutcheon's quick-draw, shoot-from-the-hip concepts make for an exciting show, but his substance is nowhere to be seen.

 

In other words, "Where's the beef?"

 

Tom Palmer

[repeater]

Hello guys, this is a great thread, and I would like to make a contribution as well.

 

I haven't read the book, and tried to understand the theory from bits and pieces gathered from here and there. Frankly I am not willing to pay for it yet, but right from the start I found the ideas intriguing while remaining downright sceptical. The guy is overly-confident and I am sure he made some mistakes, but I don't believe one can call him a fullblown crank. His work is controversial for sure, and is perhaps not of serious scientific worth, but at least is a creative way to view the world. Made my head bend.

 

Here are a few links I found, if anyone is interested:

http://en.wikipedia.org/wiki/Expansion_theory

An explanation of the basic concepts.

 

http://homepage.mac.com/ruske/ruske/finaltheory.html

A conversation between an engineer and the author. The one is not convinced, since the way orbits work in this new theory eludes him. The result: A dealbreaker. Yes, eluding me as well.

 

Tom Palmer: Is this beef?

In this pretty cranky review of the book at http://www.dpedtech.com/FTreview.pdf, one finds the following paragraph:

 

"In his whole book he only calculates one original number -- his atomic expansion constant of Xa = 7.7x10^-7 s^-2. He uses Galileo's constant acceleration equation d = a t^2 / 2, where d is the distance an object falls. For 1 second he gets a / 2 = (9.8 / 2) m/s^2 = 4.9 m/s^2. He uses an earth radius of 6.37x10^6 m.

The ratio (4.9 m/s^2) / (6.37x10^6 m) comes pretty close to his Xa value. Then he

devises a formula for taking into account the various relative changes involved in

expanding bodies. Unfortunately he only gives us one example applying that constant:

his calculation of atomic hydrogen's expansion (pp. 192-193). (We can not use his

argument about the tunnel through the earth, p. 105.) To find G in terms of a hydrogen

atom's radius and mass McC uses the formula R^3 / Xa = G M, where M is a proton's

mass (1.67x10^-27 kg) and R is the hydrogen radius (5.29x10^-11 m). He gets G =

6.8x10^-11 m^3/s^2 kg. McC's constant Xa seems to function rather like G in

Newtonian calculations. It is a universal constant applied to local variables."

 

I don't quite know any more that what is stated here, but I assume there is a coherent argument for the equations. Perhaps he is just playing with numbers, and perhaps the above comes down to A = A, but relating the hydrogen's mass and radius to G is striking.

 

If I understand it correctly, current science cannot give an account for the value of the G constant. Well victory is short lived, because it seems here he simply introduced another! Interesting nonetheless.

[CraigD]

Thanks for the links, Repeater. I found http://homepage.mac.com/ruske/ruske/finaltheory.html very informative. The idea of gravity as actual acceleration due to expansion of space was one I had no inkling of from my read of the first chapter of McCutcheon’s “The Final Theory”, which is available free of cost on the author’s website. I continue to conclude, as Ruske does, that TFT is fundamentally flawed, beyond hope of repair.

 

An interesting quality of TFT is that, unlike clear “crank” theories, it is a genuinely scientific theory – it allow one to make predictions that may be experimentally falsified. Unlike some of the more well-known Theories of Everything and Grand Unified Theories, falsifying experiments for TFT require only modest experimental resources, ones within the reach of anyone with access to a college or good high school lab.

 

A prediction of TFT is that F=G*m1*m2/r^2 does not hold. Ruske suggests that it has been shown to hold in experiments using the earth as m1, a test object for m2, and varying r by choosing test sites at different altitudes. Others cited data contradicting this.

 

As I understand it the gravity described by TFT should be measurable by the classic Cavendish torsion bar experiment. (I mentioned this earlier in this thread, in reference to chapter 1’s testing different substances to see if some have more gravitational attraction for the same mass. I believe now I was mistaken that it was making that claim) One can easily vary r by very large ratios in this experiment, producing a high-precision plot of F vs. r.

 

Does anyone know of a public dataset for this experiment?

[Erasmus00]

Thanks for the links, Repeater. I found http://homepage.mac.com/ruske/ruske/finaltheory.html very informative. The idea of gravity as actual acceleration due to expansion of space was one I had no inkling of from my read of the first chapter of McCutcheon’s “The Final Theory”, which is available free of cost on the author’s website. I continue to conclude, as Ruske does, that TFT is fundamentally flawed, beyond hope of repair.

 

You should also note that in McCutcheon's theory, expansion is related to density, so not all objects fall at the same rate. Lunar Ranging experiments, and Eotvos experiemnts, however, prove him utterly wrong.

-Will

[ldsoftwaresteve]

Erasmus: You should also note that in McCutcheon's theory, expansion is related to density, so not all objects fall at the same rate. Lunar Ranging experiments, and Eotvos experiemnts, however, prove him utterly wrong.

I was under the impression that you had not read the book, Will. Could you point me to the part of the book that says that?

[Tom Palmer]

Tom Palmer: Is this beef?

In this pretty cranky review of the book at http://www.dpedtech.com/FTreview.pdf, one finds the following paragraph:

 

"In his whole book he only calculates one original number -- his atomic expansion constant of Xa = 7.7x10^-7 s^-2. He uses Galileo's constant acceleration equation d = a t^2 / 2, where d is the distance an object falls. For 1 second he gets a / 2 = (9.8 / 2) m/s^2 = 4.9 m/s^2. He uses an earth radius of 6.37x10^6 m.

The ratio (4.9 m/s^2) / (6.37x10^6 m) comes pretty close to his Xa value. Then he

devises a formula for taking into account the various relative changes involved in

expanding bodies. Unfortunately he only gives us one example applying that constant:

his calculation of atomic hydrogen's expansion (pp. 192-193). (We can not use his

argument about the tunnel through the earth, p. 105.) To find G in terms of a hydrogen

atom's radius and mass McC uses the formula R^3 / Xa = G M, where M is a proton's

mass (1.67x10^-27 kg) and R is the hydrogen radius (5.29x10^-11 m). He gets G =

6.8x10^-11 m^3/s^2 kg. McC's constant Xa seems to function rather like G in

Newtonian calculations. It is a universal constant applied to local variables."

 

I don't quite know any more that what is stated here, but I assume there is a coherent argument for the equations. Perhaps he is just playing with numbers, and perhaps the above comes down to A = A, but relating the hydrogen's mass and radius to G is striking.

Thanks, Repeater, for filling in some blanks for me. I hadn’t encountered anything previously to indicate that Mark McCutcheon (hereinafter McC) included any original mathematical derivations in his opus. I appreciate the links, and your transcribing the mathematical “atomic expansion constant” paragraph from Douglass A. White’s detailed review, which I have consulted.

 

I was initially impressed that McC had at least managed to come up with a definite figure to quantify one of his claims. He also seemed to carefully keep the physical dimensions (mass, length, time) balanced in his equations. So far, so good.

 

I tried to keep my negative impressions at bay and give the guy a chance to convince me, and not come off as a closed-minded bigot (or “dyspeptic skeptic”). After all, you described White’s review of McC’s book as “pretty cranky,” whereas I thought the gentleman was pretty tolerant (although he never missed a chance to tout his own theory at McC’s expense).

 

So I waded into McC’s math, checking and analyzing. First, let’s review how McC comes up with his “atomic expansion constant” Xa:

 

At the surface of the earth, the distance an object falls is given, quite correctly, as d = a t^2 / 2 m. The constant “a” is 9.8 m/s^2, so let’s rewrite the equation as d = 4.9 t^2 m. The constant factor 4.9 has the physical dimensions of acceleration, i.e., m/s^2 (meters per second per second). This gives us (4.9 m/s^2), which McC then divides by the earth radius (6.37x10^6 m). This ratio is his Xa. (I’m not clear on whether McC also derives Xa by some other means, because White says only that this ratio “comes pretty close to his Xa value.”)

 

Since Xa is allegedly a “universal constant” (White), the same ratio Xa should result when the preceding steps are applied to all other heavenly bodies. (This is because this “universal” ratio is derived from two distinctly non-universal quantities that vary, sometimes considerably, from one body to another.)

 

For example, the corresponding ratio Xa at the surface of the moon would be (1.62 m/s^2) / (1.738 x 10^6). Its “Xa” would therefore be 9.32 x 10^-7 s^-2, which is over 20 percent larger than the “Xa” at the surface of the earth. Not exactly a “universal constant.”

 

However, White adds this cryptic remark: “Then he [McC] devises a formula for taking into account the various relative changes involved in expanding bodies.” Although virtually devoid of any clear, meaningful content, this sentence might be hinting at some means by which McC attempts to reconcile the varying “Xa” values. If so, McC’s track record would suggest to me that it would be yet another of his disingenuous little side-stepping finesses when faced with a looming contradiction. But I’ll withhold further judgment on that until I get some clarification as to just what McC does do about this otherwise intractable problem.

 

Now, a cautious disclaimer: Is there something I missed in McC’s derivation that would account for what might turn out to be only an apparent discrepancy? Is the error only a result of a faulty transcription? Is The Final Theory correct, but only the Douglass A. White review (my source) erroneous in its summary? I don’t want to put a “bum rap” on anyone.

 

Whatever the case, there are other problems with McC’s math. His derivation of G is based in part on the radius of the hydrogen atom, which he gives as (5.29 x 10^-11 m). I find it interesting that, despite his sweeping criticisms of modern physics, he trustingly employs their results when these can serve his purposes.

 

But the catch is: The hydrogen atom does not have a sharply defined radius (except when treated as a classical object for convenience’s sake). Quantum-mechanically, the orbital electron is smeared out (three-dimensionally) in varying spatial configurations, depending on the energy level and orbital angular momentum. Rather than belabor the point, I refer the reader to this web page: http://www.ufoarea.com/physics_cosmology_intro_quantum_mechanics.html

 

On that page, look at Figure 6-12, just a short way past the top of the page. Then tell me: Which of these probability density plots shows “the” radius of the hydrogen atom? And even if you manage to pick one, tell me where its precise outer boundary is. I think you’ll see the point.

 

Repeater, you wrote that “relating the hydrogen’s mass and radius to G is striking.” If you look closely, you may see that McC has not truly related these quantities, but only appears to. What he has done is come up with a numerical hash that includes his Xa and conveniently matches G in physical dimensions and in value to two significant digits (6.8 x 10^-11 m^3/s^2 kg), which, although a neat trick, actually proves little by itself. And it won’t fly, until he can overcome the intrinsic quantum uncertainties (which I’m sure he denies) that blur the very concept of a definitive hydrogen radius.

 

But even if it were somehow possible to get a precise hydrogen radius, it is well to remember that physicists are routinely bedeviled by what science calls “numerical coincidences.” It takes more than a mere number match (especially a shaky one like this) to prove strict equivalence.

 

I have other thoughts, but I’ll hold them for now.

 

Thanks again, Repeater, for your posting. As to your question, “Is this beef?” - I can only answer that, in my opinion, any restaurant serving it would be shut down by the health department. But I’ll respect your view, whatever it may be. And I’ll welcome any honest criticisms or valid corrections from anyone.

 

Tom Palmer

[Erasmus00]

I was under the impression that you had not read the book, Will. Could you point me to the part of the book that says that?

 

I haven't read the book, I was using the formula provided from McCutcheon by someone else in this thread: a(t0) = -2*(R1 + R2 + y0)*7.7X10^(-7).

R1 and R2 are radii of the gravitating objects. y0 is the distance between them.

 

Notice the relative acceleration between the two bodies depends on the size of the two bodies (hence the density). In McCutcheon's theory, then, objects fall at different rates.

 

Also notice that McCutcheon's theory (unlike every other theory of gravitation) doesn't come near an inverse square law with distance (which is why I gave up entirely on the theory, luckily without purchasing the book).

-Will

[repeater]

Hi Tom, thanks for your post

 

Thanks, Repeater, for filling in some blanks for me. I hadn’t encountered anything previously to indicate that Mark McCutcheon (hereinafter McC) included any original mathematical derivations in his opus. I appreciate the links, and your transcribing the mathematical “atomic expansion constant” paragraph from Douglass A. White’s detailed review, which I have consulted.

 

I was initially impressed that McC had at least managed to come up with a definite figure to quantify one of his claims. He also seemed to carefully keep the physical dimensions (mass, length, time) balanced in his equations. So far, so good.

 

This equation paragraph kept my eyes glued to the theory for a while longer, beyond the theory's aesthetic strangeness. It is unforunate that this is not mentioned at any other discussion of this book that I've witnessed. If an alternative theory is to survive, it will have to make strong statements like these, and challenge the scientific status quo further by analysing experimental data.

 

Otherwise the only impression is of a downloadable chapter one rhetoric that reprimands science's heroes and gives no mention of the theory at all.

 

I tried to keep my negative impressions at bay and give the guy a chance to convince me, and not come off as a closed-minded bigot (or “dyspeptic skeptic”). After all, you described White’s review of McC’s book as “pretty cranky,” whereas I thought the gentleman was pretty tolerant (although he never missed a chance to tout his own theory at McC’s expense).

 

So I waded into McC’s math, checking and analyzing. First, let’s review how McC comes up with his “atomic expansion constant” Xa:

 

At the surface of the earth, the distance an object falls is given, quite correctly, as d = a t^2 / 2 m. The constant “a” is 9.8 m/s^2, so let’s rewrite the equation as d = 4.9 t^2 m. The constant factor 4.9 has the physical dimensions of acceleration, i.e., m/s^2 (meters per second per second). This gives us (4.9 m/s^2), which McC then divides by the earth radius (6.37x10^6 m). This ratio is his Xa. (I’m not clear on whether McC also derives Xa by some other means, because White says only that this ratio “comes pretty close to his Xa value.”)

 

Since Xa is allegedly a “universal constant” (White), the same ratio Xa should result when the preceding steps are applied to all other heavenly bodies. (This is because this “universal” ratio is derived from two distinctly non-universal quantities that vary, sometimes considerably, from one body to another.)

 

For example, the corresponding ratio Xa at the surface of the moon would be (1.62 m/s^2) / (1.738 x 10^6). Its “Xa” would therefore be 9.32 x 10^-7 s^-2, which is over 20 percent larger than the “Xa” at the surface of the earth. Not exactly a “universal constant.”

 

That is not a good indication yes.

 

But I'm afraid there is some bad news: It is McC's opinion that Newton's Law of Gravitation does not hold. ;)

 

The motions of the planetary bodies are related to their expansion, not their mass per se. So while the current calculated values of their masses fit Newton's model, and it is a good approximation, it does not necessarily have that value. So in short, we don't know the masses of planetary bodies at all!

 

My opinion: It is terribly difficult to argue with a person if he discounts half of our physics.

 

However, White adds this cryptic remark: “Then he [McC] devises a formula for taking into account the various relative changes involved in expanding bodies.” Although virtually devoid of any clear, meaningful content, this sentence might be hinting at some means by which McC attempts to reconcile the varying “Xa” values. If so, McC’s track record would suggest to me that it would be yet another of his disingenuous little side-stepping finesses when faced with a looming contradiction. But I’ll withhold further judgment on that until I get some clarification as to just what McC does do about this otherwise intractable problem.

 

Now, a cautious disclaimer: Is there something I missed in McC’s derivation that would account for what might turn out to be only an apparent discrepancy? Is the error only a result of a faulty transcription? Is The Final Theory correct, but only the Douglass A. White review (my source) erroneous in its summary? I don’t want to put a “bum rap” on anyone.

 

I think it would really be great if ldsoftwaresteve could be so gracious to confirm if this is so.

 

Whatever the case, there are other problems with McC’s math. His derivation of G is based in part on the radius of the hydrogen atom, which he gives as (5.29 x 10^-11 m). I find it interesting that, despite his sweeping criticisms of modern physics, he trustingly employs their results when these can serve his purposes.

 

But the catch is: The hydrogen atom does not have a sharply defined radius (except when treated as a classical object for convenience’s sake). Quantum-mechanically, the orbital electron is smeared out (three-dimensionally) in varying spatial configurations, depending on the energy level and orbital angular momentum. Rather than belabor the point, I refer the reader to this web page: http://www.ufoarea.com/physics_cosmology_intro_quantum_mechanics.html

 

On that page, look at Figure 6-12, just a short way past the top of the page. Then tell me: Which of these probability density plots shows “the” radius of the hydrogen atom? And even if you manage to pick one, tell me where its precise outer boundary is. I think you’ll see the point.

 

Repeater, you wrote that “relating the hydrogen’s mass and radius to G is striking.” If you look closely, you may see that McC has not truly related these quantities, but only appears to. What he has done is come up with a numerical hash that includes his Xa and conveniently matches G in physical dimensions and in value to two significant digits (6.8 x 10^-11 m^3/s^2 kg), which, although a neat trick, actually proves little by itself. And it won’t fly, until he can overcome the intrinsic quantum uncertainties (which I’m sure he denies) that blur the very concept of a definitive hydrogen radius.

 

A good point. I erronously assumed he meant "proton radius", which would be accurately measurable.

 

By the way, McC rethinks the entire subatomic world in expansive terms, but I think I'll restrict my interest to his view of simple gravity.

 

But even if it were somehow possible to get a precise hydrogen radius, it is well to remember that physicists are routinely bedeviled by what science calls “numerical coincidences.” It takes more than a mere number match (especially a shaky one like this) to prove strict equivalence.

 

The dangers of numerology. As that review stated, "Unfortunately he only gives us one example", and I concur.

 

An impressive trick to pull out of your hat, I'll give you that. But the fact that this number follows from what I assume is a detailed reasoning process makes him very lucky indeed. And I must confess still leaves me wondering a bit.

 

I have other thoughts, but I’ll hold them for now.

 

Thanks again, Repeater, for your posting. As to your question, “Is this beef?” - I can only answer that, in my opinion, any restaurant serving it would be shut down by the health department. But I’ll respect your view, whatever it may be. And I’ll welcome any honest criticisms or valid corrections from anyone.

 

Tom Palmer

 

A pleasure. It seems it may be something approaching horse meat then? ;)

 

I like the theory because of its way of visualizing gravity, and it is a completely different way of viewing the universe. Unfortunately, in scientific terms that isn't enough. This equation is something that seems substantial and I'm glad we could talk about it.

 

Salutations!

[repeater]

Hi Will

 

I haven't read the book, I was using the formula provided from McCutcheon by someone else in this thread: a(t0) = -2*(R1 + R2 + y0)*7.7X10^(-7).

R1 and R2 are radii of the gravitating objects. y0 is the distance between them.

 

Notice the relative acceleration between the two bodies depends on the size of the two bodies (hence the density). In McCutcheon's theory, then, objects fall at different rates.

 

Also notice that McCutcheon's theory (unlike every other theory of gravitation) doesn't come near an inverse square law with distance (which is why I gave up entirely on the theory, luckily without purchasing the book).

 

If I got it right, the expansion is accelerating. That is why an object falls to the earth at an accelerated pace. (If you are looking for an inverse square law of force...according to the theory there is no gravitational force it seems. Simply objects moving closer to each other due to expansion).

 

If everything is accelerating though, I still get the feeling that everything will soon be smashed into another. The issue of orbits is for me a problematic matter.

[ldsoftwaresteve]

Erasmus: I haven't read the book

And I guess that's my point Will. Nowhere in his book does he relate expansion to density. He relates it specifically to size only. The only time he brings up density is in the context of a bodie's makeup and he shows that the expansion of the body relative to an outside frame of reference is affected by the distribution of the mass inside of the expanding body.

You seem to take every opportunity to brag about how you haven't read the book and the part that confuses me is that the value of your time would seem to be greater than the value you'd spend to get the book and be done with it. At least then you could maintain the pretense of being fair.

[Tom Palmer]

My opinion: It is terribly difficult to argue with a person if he discounts half of our physics.

 

The dangers of numerology. As that review stated, "Unfortunately he only gives us one example", and I concur.

 

An impressive trick to pull out of your hat, I'll give you that. But the fact that this number follows from what I assume is a detailed reasoning process makes him very lucky indeed. And I must confess still leaves me wondering a bit.

 

A pleasure. It seems it may be something approaching horse meat then? ;)

Hello, Repeater.

 

Thanks for the kind reply. "Horsemeat" - I couldn't have put it better, myself! :)

 

Earlier today, I spent some time duplicating the McC calculations that yield G, the universal constant of gravitation. I had another posting all set to be submitted, in which I thought I had demonstrated his calculations to be utterly wrong on all counts.

 

However, I couldn’t quite make myself believe that McC could have been so careless or incompetent as to miscalculate G by a factor of over a trillion, so I decided I’d better give him the benefit of the doubt and see if my source - Douglass A. White’s review of his book - might be at fault rather than The Final Theory. In a word, it turns out it probably was.

 

As you know, White gives the basic McC formula as R^3 / Xa = G M, where R is the hydrogen radius, Xa is McC’s “atomic expansion constant” and M is the proton’s mass. As given by White, this formula simply doesn’t work, or even come close. Not only is it quantitatively off by some twelve orders of magnitude, but its physical dimension for time is also wildly off.

 

So I sat down and tried to rework the formula to see if, using the same parameters, there was a different combination that does yield a close match to G, both quantitatively and dimensionally. And I found it. McC’s intended formula is apparently R^3 x Xa = G M. In other words instead of dividing R^3 by Xa, the two values should be multiplied together.

 

So, solving for G, the “correct” form would be G = (R^3 x Xa) / M. I would be curious to know if McC’s book itself shows the base formula correctly, as R^3 x Xa = G M (which could also be written R^3 / M = G / Xa, etc.), or if the erroneous form originated in the book rather than in White’s review.

 

I certainly don’t mean to promote the book or in any way suggest that the problems I previously discussed can be ignored but, in the interest of fairness, I felt that the apparently faulty transcription of McC’s formula by White should be recognized and corrected. In my opinion, McC has enough legitimate challenges to his theory to contend with--he shouldn’t have to be further distracted by bogus ones.

 

Best regards.

Tom Palmer

[Erasmus00]

And I guess that's my point Will. Nowhere in his book does he relate expansion to density. He relates it specifically to size only. The only time he brings up density is in the context of a bodie's makeup and he shows that the expansion of the body relative to an outside frame of reference is affected by the distribution of the mass inside of the expanding body.

 

The formula I quoted is either valid or it is not. If it is the formula McCutcheon provides (and I have no reason to doubt this) then why shouldn't I be able to use it to do an analysis regardless of wether I've read the book? According to McCutcheon, there is no equivalence between gravitational and inertial mass. Eotvos and Lunar Ranging experiments, however, prove him quite wrong.

-Will

[ldsoftwaresteve]

Erasmus: The formula I quoted is either valid or it is not.

Will, I bow to your superior understanding of mathematics, however, if the formula implies that the amount of expansion is relative to the density of an object, then it doesn't represent what McCutcheon theorizes, assuming I understand McCutcheon correctly of course.

[Tom Palmer]

But the fact that this number follows from what I assume is a detailed reasoning process makes him very lucky indeed. And I must confess still leaves me wondering a bit.

Friend Repeater,

 

I hear you. It does seem to be too much to ask of coincidence that McC is seemingly able to compute, quite correctly, the value of G (the universal constant of gravitation) using his “atomic expansion constant “ Xa ([1]gravitational acceleration at surface of the earth divided by [2] the earth’s radius), along with two other known quantities ([3] classical radius of the hydrogen atom and [4] mass of the proton/hydrogen atom).

 

I write “proton/hydrogen atom” because virtually the entire mass of hydrogen (for its primary isotope) is contained in its one-proton nucleus, and so, including or excluding the orbital electron doesn’t affect the results within McC’s limits of accuracy (i.e., between 2 and 3 significant digits). The proton contributes almost 99.95% of the hydrogen atom’s total mass.

 

I spent a good part of this past weekend doing detailed calculations, being careful to avoid guesswork and “logical leaps,” but just sticking to the mathematics of the thing. I simply analyzed (in excruciating detail) just what it is about those four quantities that can yield G so well.

 

Now I’ll give you the bottom line, then give you a calculation you can perform in order to see for yourself.

 

After much toil, I ended up with a single equation ready to be evaluated. If both sides turned out to be exactly equal, then McC’s formula would yield the exact value of G. I excitedly undertook the evaluation of both sides of my formula, being careful to get it right.

 

It turned out that the two sides weren’t exactly equal, but they were within 2 percent or so of exact equality–extremely close, close enough to assure that McC’s formula for G would match the true value of G to about two significant digits, perhaps three, depending on how the rounding was done. That’s the bottom line.

 

Here is that equation I ended up with:

 

>>> R^3 / r^3 = 2 M / m <<<

 

R = radius of the hydrogen atom (classical) 5.29 x 10^-11 m

r = radius of the earth 6.37 x 10^6 m

M = mass of the proton/hydrogen atom 1.67 x 10^-27 kg

m = mass of the earth 5.976 x 10^24 kg [britannica]

 

You might wonder about that last one (“mass of the earth”), since it doesn’t appear anywhere in McC’s calculations--neither in Xa, nor in his formula for G. But it turns out that it is in there implicitly, thanks to the quantities “one-second acceleration at surface of the earth” and “radius of the earth” (which defines the distance from the gravitational center to the surface at which the acceleration takes place). At one point I had to employ the basic formula “F = ma” (force equals mass times acceleration), courtesy of Mr. Newton. That cracked the case for me, because it reduced everything to that simple formula of dimensionless ratios that I just gave you.

 

To put it in plain terms,

 

The volume of the hydrogen atom divided by the volume of the earth is roughly equal to two times the mass of the hydrogen atom divided by the mass of the earth.

 

Feel free to try your hand at calculating it. [Of course, the left-hand side can be written (R / r )^3, so you only have to cube one quantity. Also, note “volume,” not “radius.”]

 

Here’s what I get:

 

5.73 x 10^-52 = [almost] 5.58 x 10^-52

 

The left-hand side is about 1.02 times the right side. An exact match might have been very significant. But, as they used to say, “Close, but no cigar.” I realize I haven’t given you the whole derivation of my little formula - it is quite involved, so I felt I was sparing both of us by omitting it, at least at the outset. However, it is the “proof of the pudding,” so if you (or anyone else) wants to see the whole gory mess, I will be pleased to dutifully write it up and post it.

 

It only remains to note that the values for “radius of the earth” and “mass of the earth” (hence “acceleration at the surface”) are purely empirical, a posteriori values that can vary considerably from one planet or star to another. (Some don’t even have a well-defined surface.) So chance has played its part in giving us a home planet whose “vital statistics” bear an unusually simple relationship to the corresponding quantities of the hydrogen atom–more or less.

 

And, as I have previously mentioned, any allegedly sharply-defined “radius of hydrogen” is a convenient fiction. Its true outer boundaries are exceedingly “fuzzy” and even the shape and extent of that “fuzziness” varies with energy level, orbital angular momentum, and spin alignment. And what about all the other elements that contribute to the earth’s mass? Where do they fit in?

 

McC has found a neat little “near-coincidence,” and I’ll give him an “E for Effort” on that. But that’s all it is–a numerical near-coincidence. If he has some valid way of explaining why it doesn’t work for any known bodies other than the earth, I’m all ears. And if he has some valid way of explaining why his formula for G remains approximate even when more precise inputs are used, I’m still all ears.

 

Tom Palmer

[Tom Palmer]

But the fact that this number follows from what I assume is a detailed reasoning process makes him very lucky indeed. And I must confess still leaves me wondering a bit.

 

I spent a good part of this past weekend doing detailed calculations, being careful to avoid guesswork and “logical leaps,” but just sticking to the mathematics of the thing. I simply analyzed (in excruciating detail) just what it is about those four quantities that can yield G so well. . . .

 

I realize I haven’t given you the whole derivation of my little formula - it is quite involved, so I felt I was sparing both of us by omitting it, at least at the outset. However, it is the “proof of the pudding,” so if you (or anyone else) wants to see the whole gory mess, I will be pleased to dutifully write it up and post it.

Hello again, Repeater,

 

I’ve decided to go ahead and post the mathematical proofs I discussed in my previous posting. They’re not really too difficult - just basic algebra, plus a touch of differential calculus for determining acceleration.

 

All formulae (a spelling I grammatically call the “pretentious plural”) are in Newtonian (non-relativistic) form. Also, rather than needlessly clutter the equations with the physical dimensions for each quantity, I will just let the reader either trust that they work out correctly, or supply them him/herself.

 

I’ll start with the calculus, just to get it out of the way: “Acceleration” is determined by taking the second derivative of distance with respect to time. Briefly: At the surface of the earth, “distance” is d = 4.9 t^2 meters. The time-derivative of “d” yields “velocity”: v = 9.8 t. The time-derivative of velocity (the second time-derivative of distance) yields “acceleration”: a = 9.8, with physical dimensions of m/s^2 (meters per second per second).

 

-------GIVEN-------

 

R = radius of the hydrogen atom .... (5.29 x 10^-11 m)

r = radius of the earth .... (6.37 x 10^6 m)

M = mass of the proton/hydrogen atom .... (1.67 x 10^-27 kg)

m = mass of the earth .... (5.976 x 10^24 kg)

 

Xa = 4.9 / r .... (McC’s “atomic acceleration constant”)

R^3 Xa = G M .... (McC’s formula)

 

[Note that McC’s formula here is the corrected version that actually works,

not the incorrect “R^3 / Xa ...” shown in White’s review.

(Please see my posting #149 on 7-28-2005.)]

 

F = G m M / r^2 .... Newton’s force equation (here, the force of the earth’s

gravity on the hydrogen atom, at the surface of the earth)

F = Ma .... (the same force, expressed in terms of the resulting acceleration

of the hydrogen atom)

a = 9.8 (see “calculus” paragraph, above)

 

-------PROCEDURE-------

 

1. Solve McC’s formula for G:

... G = R^3 Xa / M

2. Substitute “Xa = 4.9 / r”:

... G = (4.9 R^3) / (M r)

3. Solve Newton’s force equation for G:

... G = F r^2 / m M

4. Substitute “F = Ma” (the M’s will then mutually cancel):

... G = a r^2 / m

5. Substitute “a = 9.8":

... G = 9.8 r^2 / m

6. Set the two expressions for G (McC’s and Newton’s) equal:

... (4.9 R^3) / (M r) = 9.8 r^2 / m

7. Divide both sides by “4.9":

... R^3 / (M r) = 2 r^2 / m

8. Shuffle the factors algebraically:

... R^3 / r^3 = 2 M / m

 

Note that “R^3 / r^3" [which can also be written “(R / r)^3"] is the ratio of the volumes of the hydrogen atom and the earth, assuming only that both have the same form—in this case, spherical.

 

Substitute the actual values for [R, r, M, m] as shown in the “Given.” The two sides will be found to closely match, but with a small discrepancy of around 2 to 2½ percent that does not vanish even when more precise values are used for the inputs. If the values for another body are substituted for the earth’s, i.e., a planet or star with a different size and density than Earth, the “close match” will generally be lost altogether.

 

Xa is most assuredly not a “universal constant” (White). Therefore, McC’s formula for G cannot possibly yield a truly constant, universal value of G at all, because it is derived from values that are not fundamental and unchanging (or mutually compensating), but were determined solely by the random vagaries that gave each individual star and planet its own particular characteristics.

 

Tom Palmer