I'm still not sure how you're computing this. I checked Nielsen's site and found a section (Sect. 17) that covers this topic http://www.rostra.dk/louis/quant_02.htm
For a star at constant mass and with decreasing G he has luminosity varying according to G^7. The relevant equation is 17.3. If I use that with the times you used before the values for SL are further increased from the ones you have. It gets really bad if we suppose like he does that the rate of G decrease itself varies (Eqn. 17.4, 17.5). But how about staying with the present hypothetical rate of decrease for now, since this is all hypothetical anyway? Will continue tomorrow.

Ah! I see why you ask the question now. Here's what I was basing the fourth-power calculation on:

"In order to remain stable via hydrostatic equilibrium, a star's luminosity increases with mass as (the star's mass)^p. The value of the exponent p varies between 3 and 4. For the rare massive stars (M* > 30 Msun), p = 3 and for the more common low-mass stars (M* < 10 Msun), p = 4."

From Nick Strobel's page on The Life and Death of Stars. Some pages give the exponent as 3.9 or even 3.5:

"The obvious point from the Mass-Luminosity relationship is that the more massive a star the more luminous is the star. Roughly speaking, we have that

L/L(Sun) ~ [M/M(Sun)]^3.9

The above exponent is based on the plot given in the text on page 357. It is just an estimate."

From the Louis Nielsen page you linked above:

"The radiation of energy from a star (or a galaxy) is known to be dependent on the mass of the star m, and the gravitational 'constant', G. It can be shown that there is the following connection between the radiated effect P and m and G."

"This relation is normally called the mass-luminosity relation:"

(17.1) P = k1 * G^7 * M^5

In Nielsen's equation, P is the "radiated effect" (I'm unclear whether this is equivalent to luminosity, L, in the previous equations); G is of course the gravitational constant (6.6 X 10^-11); M is the mass of the star; and k1 is "a system dependent proportionality constant."

I'm not familiar with the equation he gives. P'raps he's deriving an absolute energy flux and not a luminosity proportional to the current luminosity of the Sun, which is what I intended to do. But I just don't know yet.

On a University of Oregon page there's a mention of an expasion of Stefan-Boltzman law to describe luminosity in terms of radius and temperature of a star, but I don't see how this relates to Nielsen's equation. (The U of O pages are very nice, incidentally, with good graphics and some animations. I hadn't seen this set before; I'm going to do some exploring later!)

Earlier on

kilopi wrote:
Depends upon what you mean by proof. I have a friend who has, over the years, made GPS measurements in the south pacific across baselines that reach over trenches. The islands on each side of the trench are getting closer, at a rate that agrees with other plate tectonic figures. How does EE explain that?

with the link
http://www.wdcb.ru/~victat/GPS/press/paper_gps_1.html

I found a passage by Carey that might give the EE explanation of this (p. 250, Frontiers of Fundamental Physics, Barone and Selleri eds.). Carey says that where a slice of new crust has been inserted in a great circle, any segment with no new crust in it will subtend a smaller angle at the centre of the Earth. No new crust has been inserted between Hawaii and Japan since the Jurassic, so this arc appears to be shrinking at 6 cm/yr, which is what NASA finds (according to Carey). Carey says most people interpret this as being due to subduction, but he thinks it is due to new crust being inserted between Hawaii and Peru.

Carey says later on the same page that when he made queries to NASA in Virginia for GPS data that might prove his own position the data were withheld because they were considered "anomalous".

Sorry I did not reply earlier. As kilopi mentioned, Carey used the shelves not the beaches. I said that I thought Vogel also used the shelves, since he followed Carey. But I may have been partly wrong on that. In Vogel's paper in the same book mentioned in my last post, he says he got his fit on the smallest globes (less than 50 per cent present Earth radius) by using the shorelines. I am not sure what the surface area of present continental shelves worldwide is relative to total continental area, but it appears to have allowed Vogel to make his 46 per cent sphere (there is a small photo of this in the book).

Vogel states that the shelves form as the continents are torn apart. If this is true, then according to EE all the continental shelves on the Earth should look roughly similar, since they all formed in the same way. But in PT there should be some shelves that formed this way, but other shelves which look different, since they did not arise by continental breakup and were instead primordial. I was wondering what evidence there is on this. I haven't found anything yet.

Are you saying that you are not familiar with the continental shelf formations, or are you saying that all the evidence you have says that they're all the same? I'm pretty sure they're not, but maybe I'm not understanding what you mean by "different." The atlantic side of NA has a significant continental shelf, the pascific side does not.

Interesting thoughts on continental shelves! Here's an image and a bit of background from Marine Environmental and Educational Research:



"Continental shelves make up the fringes of both the oceans and continents , comprising about 7.4% of the total ocean surface, and less than 2% of the total volume of the world's oceans....The widths of continental shelves vary considerably, in some areas they are very wide (about 1500 km), while in other areas a shelf barely exists at all. On a world-wide average, the shelf is usually about 78 km wide, with the average depth of the shelf break approximately 135 meters in depth."

Now in the that map the immense continental shelves around Alaska and Siberia and the Tierra del Fuego are due to distortions in the map.

Hey, I ran across an animation from the USGS of the plate tectonics version of the breakup of Pangea:



The full page is here.

But what I read on the width of continental margins seems to suggest that in the plate tectonics model it's more likely that a continental margin bounded by a subducting plate would be narrow (see the coast of Chile). But it's not cut-and-dried, apparently; a high-stress subduction might result in uparcing of the subducting slab, and accreted sediments and island terranes might complicate the topography of a continental shelf even next to a subduction zone.

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Oh, something about stellar masses and luminosity: the relationship L ~ M^4 or L ~ M^3 seems to be derived from observation and not pure theory. As noted, stars smaller than the Sun up to about 10 times the mass of the Sun follow L ~ M^4 most closely, while much more massive stars follow L ~ M^3 more closely.

I should point out, before this is brought back up again, that there was a time before Pangea. This is not included in this animation, nor is it discussed in the EE material pointed to much earlier in this thread, where the breakup of Pangea was claimed as some sort of evidence that the Earth is expanding.

To tell you the truth, when I asked the question I forgot momentarily that Pangaea is just the latest supercontinent according to PT. Rodinia came before that and even earlier ones supposedly. Sorry, I am so used to thinking in terms of EE that I can lose track of the whole PT model. I sort of imagined for an instant a primordial Pangaean coastline formed by some totally different process. In PT of course this coast must have been formed in some earlier break-up, so perhaps it should not be too different from coastlines formed afterwards.

Note to DStahl: Thanks for the graphics and info on the shelves

According to EE the continents formed a continuous cover over the globe, which lasted up until about 250 million years ago (according to fast EE models). The idea of previous supercontinents is thus discounted in EE. In this connection, in a recent issue of Science (May 30 issue) Trond Torsvik discusses problems people are having in attempts to reconstruct Rodinia, the supercontinent immediately prior to Pangaea. Hardly a surprise that there should be problems if Rodinia never existed!

Ah, something testable.

So, for EE to be correct, there could never have been any oceans prior to the Permian (which was when Pangea started to come together).

Edited to add this link, for anyone that wants a nice overview of the history of the Earth:
Berkeley Geology Wing

This link was in the original post, also seems like a nice overview:
http://www.palaeos.com/Earth/Geography/Pangea.htm

And, ExpErdMann, I'm still waiting for the references for how the idea of impacts causing mass extinctions is losing favor.

Well, yes and no. There were no ocean basins before then, but, as mentioned a few times earlier on, there would likely have been a sea covering almost all of the planet. This sea would have been on top of the continental land masses, which were still locked together. I am assuming that the total volume of liquid water on the Earth's surface has been nearly constant over time, in keeping with the hypothesis that this water was delivered to the Earth principally by comets. Since the planet was smaller then, the depth of the sea could have been much greater than today's. When the ocean basins formed, the water drained off into them forming the oceans as we know them.

Will get you those refs. [/i]

Well, I live in upstate New York and our bedrock is dominated by Ordovician, Silurian, and Devonian (especially where I live) sedimentary rocks formed when this area was covered by a shallow sea. So in the EE model they would have to accept that portions of the "continents" were covered by ocean at that time. But you have much older Metamorphic rocks in the Adirondacks.

I would be interested in ExpErdMann's thoughts on the evidence for sedimentation dating back billions of years. The bedrock in upstate NY west of the catskills is known as the Catskill Delta and is thought to have been derived from erosion following a mountain building episode to the East. We see evidence for this in the transition of Devonian rocks from sandstones in the eastern part of the state to siltstones where I am and finally to predominately shales in the western part of the state. Can the kind of mountain formation that generated this massive deposit have originated in the EE model?

There's an interesting essay on plate tectonics versus expanding Earth, Expanding Earth? by Bill Mundy of Pacific Union College. On the subject of decreasing G, which he attributes to Van Flandern, Mundy notes some of the same concerns we've already covered:

"As applied to the earth, the idea is that if G decreases, then the earth would expand due to reduced interior gravitational pressure. But, of course, if such expansion happened for the earth it would also happen for other planets, moons and the sun. And most astrophysicists see little evidence that such expansion happened on other planets such as Mars (McElhinny, Taylor and Stevenson 1978). Also, any significant change in G during the existence of the solar system would noticeably change the planetary distances which would change the thermal environment of the earth."

One point which had puzzled me--how exactly does decreasing G cause a solid body to expand?--is also mentioned:

"Finally, calculations of the equation of state for the earth have been made in the context of general relativity (Einstein's gravitational theory) which shows that a changing G would not affect the size of the earth (Canuto 1981). Some scalar models of gravity would even have the earth shrink if G were to become smaller."

The upshot seems to be, there is no unambiguous evidence that supports a substantially decreasing G scenario and there are substantial unexplained problems with it...and there is no reason to think that a decreasing G would cause the Earth to expand anyway! I think that the best mechanism to explain an expanding Earth seems to be the change-of-state idea, or a carbide-hydride mechanism of some sort.

--------

Carey has proposed a model for mountain-building which involves a thinning of the continental crust and an upwelling of buoyant rock masses from deeper in the mantle. Mundy compares a plate-tectonics model of the Himalaya uplift with an expanding-Earth one developed by Carey:

Image: HERE (I tried embedding the image in this post, but it was too wide for comfort. Sorry.)

Isn't the summit block of Everest said to be marine limestone? It seems I read that in one of John McPhee's books...

-------

[later] Here's a NASA Q&A site which talks about satellite geodesy with respect to the expanding Earth hypothesis. The author, John L. LaBrecque, writes:

"During the last thirty years, NASA invested significantly in the development of space geodesy which uses satellites and interstellar quasars to precisely measure changes in the Earth's surface and volume. Today global space geodetic networks continuously measure the migration of continents due to seafloor spreading as well as the change in the Earth's volume. Measurements indicate that the Earth's volume has not changed more than a few millionth's of a meter/year during the past decade. Although we do not have measurements going back the millennia required to explain the prehistoric samples that you describe, geology and space geodesy point to a stable Earth volume."

To steal a line from a current movie, "Well I think that's just silly." Plate tectonic action is well supported. Driving mechanisms may not be, but that doesn't make the plate actions themselves imperfectly explained.

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So, if we run the clock backwards, at what point would there be no continental landmasses above sea level (according to EE)?

At the start of the Permian? Before? When?

Of course, I'm asking because EE is just silly, and if it makes testable predictions like this, then it will become even more obvious how silly it is.

More predictions for EE? Is Earth the only planet that is supposed to be expanding? If so, why? If not, then why is the Earth's moon obviously not expanding?

Oh, pigfeathers. I must again apologize: the material I quoted from Mundy is quite dated (1988). I got interested in reading the content and didn't look closely at the header. Furthermore, I have to caution that Mundy's hosting website may have a non-scientific ax to grind:

"The Geoscience Research Institute, founded in 1958, was established to address [the problem of finding answers to philosophical questions about our origin and destiny and about our purpose for living] by looking at the scientific evidence concerning origins. The Institute uses both science and revelation to study the question of origins because it considers the exclusive use of science as too narrow an approach. The Institute serves the Seventh-day Adventist church in two major areas: research and communication."

Nevertheless, if the data and the research can stand on its own feet, so be it no matter what the source!

Mundy writes that the mechanism of continental drift is unknown, and it seems to still be somewhat so: as kilopi wrote, mathematical models succeed only when assuming viscosities much lower than those measured. But models incorporating more complex flow regimes than simple viscous flow seem to be coming closer and closer to a good fit.

Mundy also objects that there seem to be spreading zones surrounding Antarctica but no subduction beneath the continent.

Here are some more objections to plate tectonics, from this site:

1. "The total length of spreading sites is three times longer than that of subduction sites."

Well, shooting from the hip, that's easily explained if subduction happens roughly three times as fast as spreading.

2. The heat flow problem: "According to prevailing theory the mid-ocean ridges are regions along which hot material from the mantle is upwelling to form new ocean floor as well as giving rise to the upstanding ridge topography. It is further hypothesized that as the seafloor spreads out on both sides of the ridge crest it will cool and contract. The 'lithosphere' will subside as it cools so, provided the theory is correct, increasing water depth should be associated with increasing crustal age. As the hypothesized upwelling of mantle material would be hotter than the crust, one should expect, a priori, heat flow along mid-ocean ridges to be well above the average figure for the oceanic basins, falling off at a decreasing rate with increasing cooling/distance from the ridge crest (...) However, the oceanic heat flow pattern does not readily fit the pattern anticipated by that model"On the whole, there is little difference in thermal flux between the ridge and the remaining part of the ocean.

Again, shooting from the hip, the spreading might be supposed to be much, much slower than the ability of water to conduct away the heat of the spreading center. Even the ridge itself is not in a state of constant volcanic eruption; the water conducts the heat away much faster than it is produced in new magma flows.

Yow! Way cool site: NOAA graphic of the Earth showing seafloor contours and continental shelves; you can choose to look at the globe from above the north or south poles or from a bunch of other vantage points.

Wouldn't slab pull be stronger than ridge push?

Another point regarding this concern - you have to factor all collisional boundaries into this don't you? Such as the Himalayas- although that probably doesn't do much to alleviate the discrepancy.

Nothing's perfect, right?
I'm not sure why that would have an influence on length.

I'm not even sure if I understand how the "lengths" are measured.

But, also shooting from the hip, imagine a large circle of subduction zone, with a spreading center perfectly bisecting it. Waht is the ratio of the length of the subduction zone to the length of the spreading center? Just about 3, idnit?

So the Earth's surface is just a Pi crust?

Obviously there's an enormous being or device outside that's blowing air into the earth to inflate it. Like a giant turtle. Or Planet X. Or something.

I mean, with a model like that, that explains it so perfectly, how can you argue?

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Unfortunately, we're down to about 17 ounces of the highly unstable stuff that does.

I'm sure you guys are discussing something completely different than this thought but I'll throw it in anyway.

If you look at just the Pacific Plate, the subducting side is moving faster than the opposite side. It looks as if the weight of the plate sinking is pulling. So the subducting edge is stretched, causing more earthquake activity than on the opposite side of the plate.

Well, in my simple little mind that was just a neat thought I wanted to share.

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Democracy Now! - The lost art of investigative news reporting.

I can see that you are wanting to put EE to rest ASAP! However, if you don't mind too much, I will do a little more digging before replying on this. There are a number of issues involved and I would like to get things sorted out better. I hadn't planned to get into this discussion, and so am not as prepared as I would like to be. Still I'm glad we're having it and hope it goes on awhile.

I have been painting a broad brush scenario involving (a) fixed amount of surface water on the Earth for several billion years, in accordance with the comet theory for the origins of this water; (b) a decreasing gravitational constant G, which in turn implies smaller palaeoradius; (c) fast expansion since about 250 million years ago. These ideas haven't been linked together before, and there may well be problems. It could happen I will throw up my hands and look for some other explanation for expansion.

I have checked Carey on what he thought about the sea levels in the past and his opinion is completely different than (a). He thinks water has been continuously expelled from the Earth, such that sea levels stay more or less constant over time (with some fluctuations). I find Carey's explanation a little too convenient here. I have also seen now that Jordan (a decreasing G advocate) suggested that the Earth in the Carboniferous was completely cloud-covered, such that the temperatures were relatively cool (like I suggested earlier in this thread). I would like to get more evidence on what the actual sea levels were at various times and how much land mass was known to be exposed at each time.

Let me assure you I would also like to determine if my version of EE, other versions of EE, or PT are falsifiable. That's what it's all about, right?

Looking at the Pacific Plate, which are the two opposite sides?

True, the evidence is ambiguous and there are problems, but the mechanism for the expansion in decreasing G models has not been seen as problematic. For astrophysical bodies held together by gravitation, there would be an elastic rebound as G diminishes. Conceptually, it is not too different from the rebound due to melting of the glaciers.

Might not be so. If the distance from the GPS satellite to the Earth's centre were increasing at the same fractional rate as the Earth's radius then the effects would almost cancel and NASA would be none the wiser! But such measurements could perhaps rule out a present fast expansion that was not caused by changes in G.

I've been trying to track down the assertion on the NASA Q&A site that satellite geodesy rules out expansion of the Earth over the past decade. (The problem with assertions is that they are no substitute for data and analysis!)

Researchers J. Kostelecký and A. Zeman present data and analysis in this paper, published in Acta Geod. Geoph. Hung., Akadémiai Kiadó, Budapest, Vol 35(4), pp. 415-424, 2000. Their conclusions with regard to Earth expansion:

"Computed vertical changes for individual tectonic plates - velocities are in the Table II. It is apparent from this Table that for no tectonic plate were detected statistically significant vertical change (we can not reject the zero hypothesis); the same is valid for the whole Earth in global extent. Due to accuracy, characterized by rms error 10.5 mm for global solution, we can state that if some secular vertical changes (secular expansion/contraction) exist, their absolute values must be less than 1 cm/year with statistical expectation 67%." (emphasis added)

Now, the preceding was published in 2000; a paper from M. D. Gerasimenko using data from 1979 to 1991 arrives at tentative geodetic support for an expanding Earth. Here's the abstract of Gerasimenko's paper, which is all I could find online:

"Paradoxical situation of coexistence of two hypothesis of the Earth evolution, which contradict each other (the contraction hypothesis and hypothesis of expanding Earth), is resolving by methods of modern space geodesy. The measured baseline rates from very long baseline interferometry data obtained during the period from 1979 to 1991 gives the most likely change of Earth`s radius as $\sim (+3.0\pm 0.2)\ mm/yr$. This value is in a good agreement with the hypothesis of expanding Earth based on the "hot" model. This value also explains the difference of the estimated global sea level rise +3.9 mm/yr derived from TOPEX/POSEIDON altimeter data and the tide gauge estimate of sea level rise +1.5 mm/yr due to the greenhouse effect. The agreement in these estimates obtained by the totally different techniques can be viewed as one of the arguments in favour of Solid Earth expansion model. On the other hand Smith et al. indicate that estimated space geodetic rates of plate motion are slower on average than those calculated from the global plate motion model NUVEL-1 by $6 \pm 1\%$. The value of extension of the Earth`s radius $+3.0$ mm/yr removes this discrepancy. The comparing reduced rates of plate motion determined from the LAGEOS by Smith et al. with those predicted from the model NUVEL-1 gives the slope of the best fitting line obtained from a weighted linear regression as $1.002 \pm 0.023$ for LAGEOS rates versus NUVEL-1 rates with the correlation coefficients 0.990."

I think that Gerasimenko postulates an expansion rate of 3 mm per year plus or minus 0.2 mm per year; if so, that is much less than the detection limit of the later geodetic observations (&lt; 1 cm/year).

So here's what I see as the state of play so far:

On direct evidence for expansion:

1. Recent geodetic data puts a constraint on positive vertical movement of the crust limiting any global expansion over the measurement period to less than 1 cm/year.

2. There are no direct measurements which detect a global expansion.

3. There are direct measurements of horizontal movement of the crust consistent with plate tectonics (see the first study referenced--in regard to horizontal motions, "Geophysical model responses in some cases very well to the motions verified by observations").

On mechanisms causing the expansion:

1. It appears that there is no known way for a decreasing G to cause Earth to expand, according to Canuto's work using equations of state for the Earth.

2. A decreasing G is counterindicated by several lines of evidence anyway.

-----

Now I have to crawl under the house and do some plumbing repair. Oh joy. :-?

ExpErdMann: "For astrophysical bodies held together by gravitation, there would be an elastic rebound as G diminishes. Conceptually, it is not too different from the rebound due to melting of the glaciers."

I think that's not correct. See, for example, the reference to a 1981 paper by V. M. Carnuto showing that the equations of state for Earth do not show an expansion of the Earth with decreasing G:

"It has long been assumed that if the gravitational constant G was larger in the past, the Earth's radius had to be smaller. The assertion holds provided the input from microphysics (in particular the equation of state) is independent of G. While this is true for some theories of gravity with variable G it is not so in the scale covariant theory, where the pressure can be affected by a variable G in a way that, for a constant mass of the Earth, a larger G implies a larger Earth's radius..."

Further, the analogy with glacial rebound is flawed: this is an isostatic rebound, not an expansion of the Earth beneath the rebounding continent.

Here are a few. They are all recent articles in Science, and contain refs to other papers.

"Flood Basalts - Bigger and Badder", Paul Renne, Science, 296, 1812-1819 (June 7, 2002) (Perspectives article)

"Giant Lava Flows, Mass Extinctions, and Mantle Plumes", Paul Olsen, Science, 284, 604-605 (Apr 23, 1999) (Perspectives article)

"Did Volcanoes Drive Ancient Extinctions?", Richard Kerr, Science, 289, 1130-1131 (Aug 18, 2000) (News Focus)

The idea is also discussed in the book "When Life Nearly Died: The Greatest Mass Extinction of All Time" by Michael Benton (2003)