Helium in the Atmosphere and the Age of the Earth

"The rate of influx of helium 4 from the earth's crust into the atmosphere is about 2 × 10⁶ atoms cm⁻² sec⁻¹.  The average rate of thermal escape averaged over the last solar cycle is 6 × 10⁴ atoms cm⁻² sec⁻¹.  The present abundance of helium in the atmosphere would accumulate in about two million years." — Gordon MacDonald, Reviews of Geophysics, 1963, six years before any creationist built an argument on it¹

"Under this assumption, the helium content of today's atmosphere would be almost completely primordial.  During the 10,000 years or so since its creation, less than 1% of today's helium would have been added by the decay of radioactive materials in the crust." — Larry Vardiman, stating the young-earth model in his own words, 1986²

"The problem will not go away and it is unsolved.  It appears now that He escape, like the loss of H, must occur through some process other than Jeans thermal evaporation, although much of the He loss may occur in the form of He⁺ out the open magnetic field lines over the poles." — Joseph Chamberlain, 1978.  Creationist sources quote the first sentence and stop.³

"It is evident that Jeans escape modeling does not relate adequately to physical reality; and that, contrary to claims frequently made in creationist literature, it does not provide significant evidence in support of (or contradictory to) a young-earth viewpoint." — R. H. Brown, in the Geoscience Research Institute's refereed journal Origins, 1998⁴

"For several years before the magnitude of the polar wind was determined Vardiman (1990) reported that the lack of helium in the atmosphere argued for a young earth.  That argument is no longer valid based on the measured and computed escape rate of helium to space in the polar wind." — Larry Vardiman withdrawing his own argument, at ICR, 2005⁵

Summary

Uranium and thorium in the crust decay by alpha emission.  An alpha particle is a helium nucleus.  That helium works its way to the surface and into the air.  Add up the crustal production and it comes to roughly 2 × 10⁶ atoms per square centimetre per second.  The air holds about 5.6 × 10³⁸ helium-4 atoms.  Divide one by the other and the atmosphere's whole helium inventory accumulates in under four million years, not four and a half billion.  Ordinary thermal escape carries off about 3% of what balance would require.

That calculation is correct.  It was published by a mainstream geophysicist, Gordon MacDonald, in 1963.  Melvin Cook had raised the question in Nature in 1957, and Henry Morris turned it into a young-earth argument in Scientific Creationism.

The conclusion does not follow, and the argument's own author withdrew it in print in 2005.  Five points carry the article:

1. The budget genuinely does not close, and the usual rebuttal is overstated. The best modern estimate of polar-wind escape is (3–5) × 10²⁴ atoms per second against a crustal source of (4.5–9.5) × 10²⁴. At the midpoints escape is 0.57 of the source. The figure every counter-apologetic page repeats, from Brent Dalrymple in 1984, is three to seven times too high. And the single paper the TalkOrigins index cites for closure was faulted in the mainstream literature for assuming a polar cap ten degrees too wide.
2. Even so, the arithmetic never yields a young earth. Larry Vardiman's own differential equation gives 1.76 million years, and he prints that number. Take the modern residual imbalance instead, and it still fills the present atmosphere in 6.6 million years. Six thousand years of degassing supplies 0.24% of the air's helium-4. There is no assignment of published fluxes that gives an answer under a million years.
3. The young-earth number is an assumption, not a measurement. Vardiman gets 10,000 years by supposing the atmosphere was created with essentially all its present helium already in it. Under that supposition the helium is an initial condition, and an initial condition set by fiat cannot also be a clock. John Morris says the same thing in the movement's best-known popular book, without the equations: "I suspect that the wise Creator would have included some in the original atmosphere."⁶
4. That supposition is testable, and it fails. Air runs at 1 R_A. Every candidate primordial reservoir runs 8 to 334 R_A. Two-component mixing therefore requires 88% to 99.7% of the air's helium-4 to be crustal radiogenic. Vardiman needs it under 1%. Melvin Cook named the ³He/⁴He ratio as the test in 1966 and again in 1986. He was right about the test, and the one young-earth author who eventually ran it, R. H. Brown in 1998, reached the same verdict as this article.
5. The young-earth literature retired the argument twice, and its popular literature did not notice. R. H. Brown computed 1.5 million years for the atmosphere in Origins, the Geoscience Research Institute's refereed journal, in 1998, adopted polar-wind ion escape, and wrote that Jeans-escape modelling, "contrary to claims frequently made in creationist literature," gives no support to a young earth. Larry Vardiman, who built the technical version of the argument, withdrew it at ICR in 2005 on exactly the grounds this article gives: the polar wind was measured. Answers in Genesis was still printing the argument in a book chapter in 2013.

Verdict: the anomaly was real and honestly stated in 1957 and 1963, it was answered in the right way by 1968, the answer is still only good to a factor of about two, and the young-earth conclusion never followed from the data even on its own author's arithmetic — which is what the two best-qualified young-earth authors on the subject concluded in print, in 1998 and 2005, without being pushed by anybody.

Two further things belong here because nobody else prints them.  This argument contradicts two other flagship young-earth arguments.  RATE's accelerated alpha decay would put roughly two hundred times the atmosphere's present helium into the crust in the Flood year, which is the opposite of "almost completely primordial."  And Humphreys' fifty or more Flood-year geomagnetic reversals would maximise exactly the reversal-driven escape mechanism the argument needs to rule out.

Every source this article rests on is catalogued, with what it measured and which way it cuts, in a companion page: the literature.

This is not the zircon argument

Two different young-earth arguments involve helium and they are constantly confused, including by creationists.

This one is about helium in the air.  The other is about helium retained inside zircon crystals from the Fenton Hill borehole in New Mexico, measured by the RATE project and published in 2003 and 2005.  They share one quantity, the crustal helium-4 production rate, and nothing else.  Different measurements, different physics, different failure modes, different literature.  The zircon argument is treated separately at RATE and Helium in Zircons.  Nothing here depends on it, and it is not re-argued below except where the two models contradict each other.

Where the argument comes from

1957: Melvin Cook asks the question.  Cook was Professor of Metallurgy at the University of Utah.  His letter to Nature runs one page and one column, under the title "Where is the Earth's Radiogenic Helium?"  Its opening paragraph is the passage every later writer quotes:

"AT the estimated 2 × 10²⁰ gm. uranium and 5 × 10²⁰ gm. thorium in the lithosphere, helium should be generated radiogenically at a rate of about 3 × 10⁹ gm./year.  Moreover, the (secondary) cosmic-ray source of helium has been estimated to be of comparable magnitude.  Apparently nearly all the helium from sedimentary rocks and, according to Keevil and Hurley, about 0.8 of the radiogenic helium from igneous rocks, have been released into the atmosphere during geological times (currently taken to be about 5 × 10⁹ yr.).  Hence more than 10²⁰ gm. of helium should have passed into the atmosphere since the 'beginning'.  Because the atmosphere contains only 3.5 × 10¹⁵ gm. helium-4, the common assumption is therefore that about 10²⁰ gm. of helium-4 must also have passed out through the exosphere, and that its present rate of loss through the exosphere balances the rate of exudation from the lithosphere."⁷

Cook's two numbers divide to 1.17 million years, and that is the whole of the argument in embryo.  His own preferred figure was much smaller, but it is not in Nature.  It is in his 1966 book Prehistory and Earth Models, where he takes Hurley's higher estimate of the exudation rate and gets about 12,000 years, which he calls "in remarkable agreement with the non-equilibrium radiocarbon method for dating the atmosphere."⁸  Cook confirmed that figure himself twenty years later: "I gave as my best result 12,000 years."⁹

1963: the mainstream states the problem more sharply than Cook did.  Gordon MacDonald's review in Reviews of Geophysics is the source of the two numbers the creationist literature has used ever since, and both are his.¹

"The rate of influx of helium 4 from the earth's crust into the atmosphere is about 2 × 10⁶ atoms cm⁻² sec⁻¹.  The average rate of thermal escape averaged over the last solar cycle is 6 × 10⁴ atoms cm⁻² sec⁻¹.  The present abundance of helium in the atmosphere would accumulate in about two million years.  Either some nonthermal mechanism permits at present a greater rate of escape of helium or the rate of escape has varied in time."¹

That is worth more than any creationist restatement of it.  A geophysicist writing in a review journal, with no stake in the age of the earth, laid out the imbalance and named the two ways out.

1974: Henry Morris makes it a young-earth proof.  Scientific Creationism quotes Cook's paragraph entire and then adds the sentence that has haunted the argument ever since:

"This 'common assumption,' however, is only an assumption.  There is no evidence at all that Helium 4 either does, or can, escape from the exosphere in significant amounts."¹⁰

That sentence was already false when it was printed.  W. I. Axford's paper on the polar wind and the terrestrial helium budget appeared in the Journal of Geophysical Research in November 1968, six years earlier, and proposed the mechanism the mainstream still uses.¹¹  Morris does not cite it and does not answer it.  Any modern presentation of the argument that repeats Morris is not worth a skeptic's time, and this article does not defend it.

1985: Larry Vardiman states it in ICR's popular series, and prints the million-year answer.  "Up, Up and Away!  The Helium Escape Problem" ran as ICR Impact No. 143 in May 1985.¹²  It is short, and it does not hide the number the argument actually produces:

"Using these estimated fluxes of helium, the present abundance of ⁴He would accumulate in 1.8 million years.  Only 370 thousand years would be required to supply the atmosphere with its present content of ³He.  Even in the case of ⁴He this is still 3,000 times too small."¹²

He also states the isotope problem himself, a year before Melvin Cook told him at the conference to go and study it: "If the temperature at the base of the exosphere were raised sufficiently high to explain the loss of ⁴He, the loss of ³He would still not match its influx.  In fact, it has been shown that no temperature can be maintained at which both ³He and ⁴He fluxes are in equilibrium."¹²

1986: the technical version.  Vardiman holds a PhD in atmospheric science and was at Christian Heritage College when he presented "The Age of the Earth's Atmosphere Estimated by its Helium Content" at the First International Conference on Creationism in Pittsburgh in August 1986.²  He did not pick the problem himself.  His acknowledgment reads, in full: "I wish to express appreciation to Harold Slusher for suggesting this problem."²  A 1990 ICR technical monograph followed, The Age of the Earth's Atmosphere: A Study of the Helium Flux through the Atmosphere.  That monograph could not be obtained and nothing is quoted from it below.

The 1986 conference paper is the strongest published form of the argument and the one this article answers.  It deserves credit for what it does, which is more than any later populariser: Vardiman computes the Jeans escape flux himself and gets 5 × 10⁴ atoms cm⁻² s⁻¹ at an exospheric temperature of 1500 K, names the polar wind, names solar-wind sweeping, names hot ion exchange, cites Axford 1968 by volume and page, writes down a differential equation for the inventory, and solves it.

1994: David Malcolm answers the critics.  Malcolm's reply to the Australian Skeptics in the Journal of Creation is the fullest creationist treatment in print.¹³  He re-derives Jeans escape carefully and correctly from James Walker's textbook, checks the exobase approximations, and concludes: "It certainly seems that the creationist position is correct, on the basis of the latest observational evidence."¹³

Malcolm's own answer is millions of years, and he prints it in his opening paragraph: the evidence "does indicate a young maximum age for the earth and its atmosphere (of the order of two million years), a result which is well known amongst atmospheric scientists."¹³

It is also where the argument stops developing.  Malcolm never computes a polar-wind flux.  He never quotes a number from Axford.  He disposes of every non-thermal mechanism by quoting one sentence of Walker's: "Most of these are speculative and of undetermined evolutionary significance."¹³  That sentence appears in a list that names Axford 1968, Sheldon and Kern 1972, and Torr et al. 1974, so Malcolm reproduced the citations without engaging any of them.  He was writing two years before the first detailed global calculation of ion escape was published.

1998 and 2005: the young-earth side abandons it.  R. H. Brown repudiated the argument in a refereed young-earth journal in 1998, singling out Malcolm's paper by name as the "recent example" of creationist reliance on Jeans escape.⁴  Vardiman withdrew it at ICR in 2005.  Both are treated below, because they change what this article is for.

The anomaly is real, and here is the arithmetic

Start by granting the argument everything it asks for, and check its numbers from scratch.

The inventory can be derived from two measured quantities: the mass of dry air, 5.119 × 10²¹ g, and the helium mixing ratio, 5.24 parts per million by volume.  A short Deno script does this and the rest of the arithmetic in this article; it is at research/helium-budget.ts and every input in it is labelled with its source.¹⁴

Every published figure is recovered to three significant digits.  Vardiman's own values, 3.8 × 10¹⁵ g and about 6 × 10³⁸ atoms, are 2% and 8% high, which is rounding rather than error.  There is no arithmetic cheat anywhere in this argument, on either side.

Now divide the column density by each published source flux.

One to four million years.  Jyotsna Kashyap, whose 2009 thesis is the most careful modern treatment of this problem, gets (1.9–3.9) × 10⁶ years from the same division and prints it as equation 3(a) of her introduction.¹⁵  This is not a creationist number and it is not disputed.

Against that, thermal escape is nowhere near enough.  MacDonald's solar-cycle-averaged Jeans flux of 6 × 10⁴ atoms cm⁻² s⁻¹ is 3.0% of a 2 × 10⁶ source; Vardiman's own independently computed 5 × 10⁴ is 2.5%.  Kashyap puts it in the mainstream's own words: thermal loss of ⁴He "is a factor of ~ 15 to 32 times smaller than" its production, so "it is obvious that thermal escape of He⁴ is not sufficient to account for its present concentration in the atmosphere.  Therefore there must be a non-thermal escape mechanism for helium that favours the heavier isotope."¹⁵

So the young-earth writer is entitled to all of this.  The imbalance is real, it is large, and it is stated more bluntly in the mainstream literature than in most creationist retellings of it.

The answer: helium leaves as an ion, over the poles

Above about 500 km the atmosphere is a plasma.  Solar extreme-ultraviolet light ionises neutral helium there, and Marcel Nicolet's 1961 figure for the whole-atmosphere ⁴He photoionisation rate is about 10 × 10²⁴ atoms per second, which is larger than the entire crustal source.¹⁵  So there is no shortage of helium ions.  The question is whether they can get out.

At low latitudes they cannot.  The geomagnetic field lines there are closed, and an ion that starts up one comes back down the other.  Poleward of roughly 70 to 75 degrees magnetic latitude the field lines are open to the interplanetary medium.  Electrons, being light, run ahead of the ions; the charge separation sets up an ambipolar electric field; and that field drags the light ions outward along the open lines.  This is the polar wind.  Axford applied it to helium in 1968.

Notice what this does to the creationist calculation.  Helium leaves as an ion, not as a neutral atom, and the process has nothing to do with the high-speed tail of a Maxwell-Boltzmann distribution.  Cook, Morris and Malcolm all worked the problem with Jeans escape and a Maxwellian.  They were answering a question the mainstream stopped asking in 1968.

Charge exchange is a second channel.  A neutral helium atom that swaps an electron with a hot ion in the plasmasphere becomes a fast neutral, and a fast neutral is not held by the magnetic field.  Chamberlain named it as promising, and the Torrs worked on it from 1974 onward.  Neither of those papers could be obtained for this article and no number for the channel is claimed here.

How far does the polar wind actually close the budget?

Not all the way, and this is where the counter-apologetics goes wrong.

The best modern number comes from Jyotsna Kashyap's 2009 master's thesis at the University of Calgary, supervised by Andrew Yau.¹⁵  She traced individual helium-ion trajectories from the polar ionosphere across a range of interplanetary magnetic field and geomagnetic activity conditions, took the outflow flux from satellite observations, and worked out what fraction of the ions escape rather than falling back.  Her conclusion:

"Combining the escape fraction with the outflow flux, our estimate for the escape flux is ~ (3 − 5) × 10²⁴ s⁻¹.  Comparing our estimated rate of escape to the atmospheric helium production rate of ~ (4.5 − 9.5) × 10²⁴ s⁻¹, we conclude that the polar wind is indeed a very likely mechanism to account for the balance between the sources and sinks of terrestrial helium."¹⁵

Her abstract puts it more carefully still: the escape rate "is conceivably sufficient to account for the atmospheric production rate."¹⁵  Conceivably sufficient is not balanced.

Do the division.  At the midpoints, escape is 0.57 of the source.  Across the full published ranges the ratio runs from 0.32 to 1.11, so the two overlap only at their extremes.  Add thermal escape, worth another 4% of the source, and the honest statement is this: the budget closes to within a factor of about two, with the escape side still short.

Anyone who says it balances exactly is overstating.  Anyone who says there is no escape mechanism is fifty-eight years out of date.

Where the rebuttals are wrong

This site grades both sides by the same standard, and the standard reply to this argument does not survive it.

The number everyone repeats is three to seven times too high.  Dave Matson's 1994 TalkOrigins reply to Kent Hovind is the most-cited answer, and its substance is a block quotation from Brent Dalrymple's 1984 paper for the Pacific Division of the AAAS.¹⁶

"The most probable mechanism for helium loss is photoionization of helium by the polar wind and its escape along open lines of the Earth's magnetic field.  Banks and Holzer [1969] have shown that the polar wind can account for an escape of 2 to 4 x 10⁶ ions/cm² sec of Helium-4, which is nearly identical to the estimated production flux of (2.5 ± 1.5) x 10⁶ atoms/cm² sec."¹⁶

Kashyap's (3–5) × 10²⁴ per second, spread over the earth's surface, is (5.9–9.8) × 10⁵ ions cm⁻² s⁻¹.  Dalrymple's figure of 2 to 4 × 10⁶ is three to seven times larger.  His "nearly identical" becomes, on 2009 numbers, about 57% of the source.  A reader given Dalrymple's version and then handed Kashyap's thesis would be entitled to feel misled.

The page numbers here need a caveat: this quotation is Matson's rendering of Dalrymple, cited to pages 112 and 113 of a 1984 AAAS Pacific Division proceedings volume that could not be located.  Until somebody checks the printed original, it should be read as Matson quoting Dalrymple rather than as Dalrymple verified.

Matson's own framing is worse than his source.  He opens by telling the reader that "A fair amount of helium is lost from the earth's atmosphere by simply being heated up in the elevated temperature of the exosphere," and that "In this manner about half of the Helium-3 produced is lost to outer space.  The amount of the heavier Helium-4 lost by this method appears to be far short of the amount produced."¹⁶  The second sentence is right.  The first invites a reader to think thermal escape does real work for ⁴He, and it does not: 3%.  He also describes the exosphere as the layer "beginning after the ionosphere," which gets the geometry backwards.  The ionosphere and exosphere overlap, and the overlap is exactly where the polar wind operates.

The TalkOrigins claims index is thinner still, and it rests on the wrong paper.  Claim CE001, created in February 2001, answers the whole argument in two sentences: "When ion outflow is considered, the escape of helium from the atmosphere balances its production from radioactive elements (Lie-Svendsen and Rees 1996)."¹⁷  One citation, no numbers, and the claim is attributed to Morris 1974 rather than to Vardiman.

And that one citation was faulted in the mainstream literature.  Øystein Lie-Svendsen and Manfred Rees computed globally averaged helium-ion escape over a solar cycle and concluded that "a cutoff latitude of about 60° or lower is sufficient to balance the outgassing from the Earth's crust."¹⁸  Kashyap devotes two pages to why that will not do:

"First, their assumption of a (non-drifting) Maxwellian distribution resulted in an underestimation of the ion energies … Second, the assumption of no horizontal transport neglects the significant effect of centrifugal acceleration … They found that in their case of no horizontal and vertical transport a cut-off (geographic) latitude of 60° is required for the integrated escape flux (above the cut-off latitude) to balance the ion production rate.  However, it is clear from observations … that a cut-off of 60º represents a significant overestimation of the area covered by the polar wind."¹⁵

Her own outflow area is poleward of 70 degrees invariant latitude, and she still gets within a factor of two.  But the point stands, and it is the strongest genuine move available to a young-earth writer on this whole topic: the single reference the standard counter-apologetic gives for closure is the one a later specialist says assumed too large a polar cap.

Nobody on the counter-apologetic side has answered Vardiman.  Matson mentions him in one sentence, cites the 1985 Impact piece rather than the 1986 conference paper, and says he "has not fully addressed the matter."  CE001 does not mention him at all.  The best version of this argument has never been engaged in the popular skeptical literature.  That is not a small thing to notice about a debate that has run for seven decades.

The most-quoted sentence in the dispute, in context

Every creationist treatment of atmospheric helium quotes one sentence from Joseph Chamberlain's Theory of Planetary Atmospheres.  Here is what gets quoted, and here is what the page says.

The text is identical in both editions: Chamberlain 1978 at page 278, and Chamberlain and Hunten 1987 at page 372.^{3 19}  Both were read paragraph by paragraph out of the archive.org scans, with the leaf-to-folio mapping anchored twice in each volume.

What Chamberlain means is "the quantitative budget is not yet closed."  He does not mean "no escape mechanism is known."  He names two in the next two sentences, and the first of them is the polar wind.  The paragraph immediately above on the same page gives his own numbers: the crust exhales 2 × 10⁶ atoms cm⁻² s⁻¹, against a limiting flux around 10⁸ cm⁻² s⁻¹ for a mixing ratio of 5.24 × 10⁻⁶.³

Now grade the two people who quote it, because they do not deserve the same grade.

Vardiman's use is defensible.  He writes: "None of the rates for the proposed mechanisms have been accurately quantified nor have adequate observations even begun to confirm or deny them.  Chamberlain (1978) states that the helium problem '. . . will not go away and it is unsolved.'"²  That is close to what Chamberlain means, and Vardiman had already spent three paragraphs describing the polar wind, solar-wind sweeping and hot ion exchange, and had given Axford's escape flux.  His reader is not left ignorant of the mechanisms.  This looks like ordinary compression, not concealment.

Malcolm's use is worse.  He puts it at the end of his conclusion, as the last word, immediately after asserting that "the creationist position is correct, on the basis of the latest observational evidence," and after disposing of every non-thermal mechanism by quoting one sentence of Walker's about their being speculative.¹³  A reader who finishes that article believes the escape problem has no known answer.  He also misquotes it slightly, inserting a comma: "will not go away, and it is unsolved."

Is this dishonesty?  On the evidence available, no, and it would be cheap to say otherwise.  Both writers cite the surrounding literature elsewhere in their own papers; Malcolm even reproduces Walker's citation list, which names Axford 1968 and Sheldon and Kern 1972.  The failure is not that they hid a source.  It is that they quoted a specialist's statement of residual uncertainty as though it were a statement of total ignorance, and never went back to check what the mechanisms actually deliver.  That is a real failure.  It was fixed on that side, though, and by one of their own: R. H. Brown went back to Chamberlain and Hunten in 1998, read five pages earlier than Malcolm stopped, and quoted them saying polar ion escape is "the principal means by which helium escapes from Earth."⁴  So this is the failure of an argument that stopped developing, not of an argument that lied, and the development eventually happened.

Why the conclusion still does not follow

Three steps, each stronger than the last.

Step one: the argument's own arithmetic gives 1.76 million years

Vardiman models the atmosphere's helium as a tank with a tap and a drain.  His differential equation is

dn/dt = c₁ − c₂·n

with c₁ = 2 × 10⁶ atoms cm⁻² s⁻¹ for the crustal source and c₂ = 4.54 × 10⁻¹⁶ s⁻¹ for the fractional loss rate, and n the column density.  With no helium present at the start, the solution is n = (c₁/c₂)·(1 − e^(−c₂t)).  He states the answer plainly: "the time required to reach the helium concentration of today's atmosphere would be 1.76 million years.  This period is over 2,500 times shorter than the generally assumed age of the earth."²

That is the number his own model produces.  It is not six thousand years and it is not ten thousand.

The young-earth figure enters by a different door, in the very next paragraph:

"An alternative to the long-age model, and one which runs counter to the basic assumption of the evolutionary/uniformitarian model, is that the earth's atmosphere is relatively young (less than 10,000 years).  Under this assumption, the helium content of today's atmosphere would be almost completely primordial.  During the 10,000 years or so since its creation, less than 1% of today's helium would have been added by the decay of radioactive materials in the crust."²

Read that twice, because it is the crux.  The 10,000 years is not derived from the helium.  It is assumed, and then the helium is assigned to creation to make the assumption consistent.  Under this model over 99% of the air's helium was there on day one, put there by God, and the measured inventory tells you nothing whatever about elapsed time.  A quantity fixed by fiat at t = 0 is an initial condition, not a clock.

Vardiman is candid about this and says so himself: "Since no observations of the initial conditions are available, whether the atmosphere was formed a few thousand years ago or several billion, we cannot know the original quantity of helium."²  He is right.  But that cuts his own argument's throat.  If the initial quantity is unknowable, the present quantity cannot date anything, and the paper's own conclusion, "the helium we observe in the atmosphere is primordial provides evidence that the earth's atmosphere is quite young," has the logic backwards.²  Primordial helium is an assumption of the young-earth model, not evidence for it.

This is the spine of the article.  Everything below is confirmation.

Step two: the residual imbalance still gives millions of years

Suppose the skeptic gives the creationist the whole disputed remainder.  Take the source at the midpoint of Torgersen's range, 7.0 × 10²⁴ atoms per second.  Take escape at the midpoint of Kashyap's, plus thermal escape, for 4.3 × 10²⁴ per second.  The residual is 2.7 × 10²⁴ atoms per second going into the atmosphere and not coming out.

At that rate, filling the present atmosphere from empty takes 6.55 million years.¹⁴

Run it the other way and the point is sharper.  Six thousand years of degassing at the full source rate, with no escape at all, delivers 1.33 × 10³⁶ helium-4 atoms.  The air holds 5.577 × 10³⁸.

There is no assignment of published fluxes, from any side, that yields a fill time under a million years.  So the young-earth position is not "the helium accumulated in 6,000 years."  It is "99.76% of the air's helium was there on day one."  That is a claim about creation, and the next step tests it.

Step three: the isotope ratio closes the escape hatch

Helium comes in two stable isotopes and they have completely different origins.

⁴He is what alpha decay makes.  Uranium-238, uranium-235 and thorium-232 each throw off six to eight alpha particles on the way to lead, and every one of them picks up two electrons and becomes a helium-4 atom.  So ⁴He is manufactured continuously, everywhere there is uranium or thorium.

³He is not.  No decay chain of any consequence produces it.  Terrestrial ³He is primordial, trapped in the earth when it formed, plus a small trickle from cosmic rays and tritium decay.  Its discovery venting from the mantle was reported by Clarke, Beg and Craig in 1969, and Vardiman leans on that paper as his warrant for supposing primordial helium in the air as well.²⁰

The ratio ³He/⁴He is therefore a fingerprint of where a helium sample came from, and it is measured in units of the atmospheric value, R_A = 1.39 × 10⁻⁶.

Now do the mixing.  If the air's helium is a two-component mixture of crustal radiogenic helium and some primordial reservoir, then by ⁴He amounts

R_air = f_crust · R_crust + (1 − f_crust) · R_primordial

and there is exactly one value of f_crust that lands on 1 R_A for each choice of primordial end-member.

Vardiman needs the crustal-radiogenic share to be under 1%.  The isotope ratio requires it to be at least 88%, and at least 99% for any end-member that is primordial in a recognisable sense.  The two requirements are two orders of magnitude apart, in the wrong direction.

Put plainly: the air's helium is isotopically crustal.  It looks exactly like the product of a long history of uranium and thorium degassing, and nothing at all like a reservoir stocked at creation from the same material the planet was made of.  This is not an inference from the age of the earth.  It is a measurement, made on air and on rocks, and the mixing arithmetic is a line of algebra a reader can redo in a minute.

Melvin Cook saw this coming, and he saw it in 1966.  Twenty years before the conference, in the book where his own 12,000-year figure lives, he put the isotope ratio on the table and said what it implied: "An important experimental fact bearing on this problem is that the He³/He⁴ ratio in the atmosphere is twelve times greater than in natural gas. … If helium were being lost from the atmosphere, this ratio should be lower in the atmosphere than in the earth, or in natural gas.  This result, on the other hand, is strongly suggestive of an external source of terrestrial helium."⁸

He also proposed the escape hatch, and it does not hold.  Cook's answer was that the air's ³He is topped up from space, by "terrestrial accretion of meteoric materials which are known to have occluded helium with a very high ratio of helium-3 to helium-4 (up to 0·3)."⁸  That is a real proposal and it deserves a number rather than a dismissal.  R. H. Brown supplied one in 1998, from the young-earth side: interplanetary dust arrives at about 4 × 10⁴ tons a year carrying an average 6.8 × 10¹⁴ ³He atoms per gram, which is 136 grams of ³He per year.⁴  The air holds 3.88 × 10⁹ g of ³He.  At Brown's rate that is a fill time of 28.5 million years, and 6,000 years of it supplies 0.021% of the air's ³He.¹⁴  Cook's source is real and far too slow, in the same direction and by the same margin as everything else here.

And Vardiman offered a second hatch, a vapour canopy.  In 1985 he wrote that "Today's observed concentration of ³He may have been strongly affected if the earth were surrounded by a water vapor canopy until about 4000 years ago … The concentration of ³He would have been much greater if a vapor canopy existed, resulting in a high residual concentration today."¹²  That was offered for a different problem — his own arithmetic fills the air's ³He in only 370,000 years — and it makes the ratio problem worse rather than better.  Extra cosmogenic ³He pushes the air's ratio up, away from the crustal value, and the ratio is already too high for a mostly-primordial atmosphere by two orders of magnitude.  And a canopy that vanished 4,000 years ago is not testable against anything now observable, so the hatch cannot be closed or opened by measurement, which is a poor foundation for a claim about ages.

Both hatches are recorded because it would be wrong to say the young-earth side never answered the isotope objection.  It answered twice, in 1966 and 1985, and neither answer survives contact with a flux.

Cook repeated the point at the conference.  In his signed Discussion of Vardiman's 1986 paper he wrote that Axford's polar wind "might conceivably be nearly accounted for" as a total helium loss, "but certainly not the ratio He3/He4 in the lithosphere vs. atmosphere vs. exosphere," and added: "I think the article by Dr. Vardiman would have been improved by a more careful study of the He3/He4 ratio for different conditions on the earth.  This may well be where we must look."⁹  Vardiman agreed in his printed Closure: "I agree with him that the He3/He4 ratio is probably the most fertile ground for further study.  I'm sorry I wasn't able to contribute more in that regard."²

The test was eventually run on that side, and it came out the same way.  Neither principal ran it.  R. H. Brown did, in Origins in 1998, and concluded that a created atmosphere would require "the creation of at least two types of helium, each with a distinct primordial He-3/He-4 ratio, differing by several orders-of-magnitude.  This seems unlikely.  There is no evidence for the creation of any other element in this manner."⁴  That is the objection above, reached independently by a young-earth author writing in a young-earth journal, and it is one of two reasons the next section exists.

And ³He is a second clock that gives the same answer

Mid-ocean ridges vent primordial ³He into the deep ocean and thence into the air.  The published flux estimates have come down over time: Craig and colleagues got 1070 ± 270 mol/yr in 1975, Bianchi and colleagues 527 ± 102 mol/yr in 2010, and Reiner Schlitzer's own data-assimilation fit 450 ± 50 mol/yr in 2016.²¹  Divide the atmospheric ³He inventory by each:

One to three million years, from a completely different measurement.  And here is the part that is hard to escape.  ³He has no budget anomaly: it escapes thermally at very nearly the rate it is produced, because it is lighter.  MacDonald's own figures are an influx of about 10 atoms cm⁻² s⁻¹ against an escape of about 4; Kashyap's are that thermal loss and production are the same order.¹¹⁵  So the isotope with the escape problem and the isotope without one give the same few-million-year residence time.

A steady-state atmosphere produces that coincidence automatically.  A young atmosphere has to produce it by having been stocked at creation with two isotopes in exactly the proportion that steady state would have reached, which is a coincidence nobody has offered a reason for.

The young-earth literature retired this argument twice

Everything above is a case made from outside.  The same case was made from inside, twice, in young-earth journals, and the popular literature did not follow.

1998: Origins prints the arithmetic and the repudiation

R. H. Brown published "Unique Enigmatic Helium" in Origins 25(2) in 1998.⁴  Origins is the refereed journal of the Geoscience Research Institute, the research arm of Seventh-day Adventist creationism; Brown was a physicist there, and his paper thanks Benjamin Clausen, Paul Giem and Clyde Webster along with unnamed reviewers.  This is not a blog post.  It is nineteen pages with tables, and it works the budget from raw quantities the way this article does.

His numbers, and they are the same numbers.  The crust holds 1.9 × 10¹⁴ kg of ⁴He against a production of 2.5 × 10⁶ kg a year, "about 80 million years of radiogenic accumulation."  The atmosphere holds 3.8 × 10¹² kg of helium, and:

"To produce this amount of helium by the radioactive decay in the crust would require over 1.5 million years.  Additional accumulation time would be required to account for loss from the atmosphere into outer space."⁴

And he checks whether the number moves the helpful way.  It does not.  Cut the crustal production rate to a tenth and the fill time goes up to 15 million years, not down.⁴

He adopts the mechanism.  Brown lists seven non-thermal escape processes, five of which involve ions, and writes that "Ion escape at the magnetic poles where there is no transverse acceleration of a moving charged particle is considered by Chamberlain and Hunten to be the principal means by which helium escapes from Earth."⁴  That is the polar wind, named by a young-earth author in a young-earth journal, four years after Malcolm dismissed the whole class of mechanisms as speculative.

And he says the argument is dead.  His conclusions:

"It is evident that Jeans escape modeling does not relate adequately to physical reality; and that, contrary to claims frequently made in creationist literature, it does not provide significant evidence in support of (or contradictory to) a young-earth viewpoint."⁴

Note the second half of that sentence, because it is the more honest half.  Brown is talking about the Jeans-escape model in particular, and about that model he says the evidence cuts neither way — it does not support a young earth and it does not refute one.  That is a more careful position than either side of the popular dispute has taken.

What Brown keeps.  He does not end up an old-earther.  He substitutes a different helium argument — excess ³He retained in minerals, which he thinks diffusion should have emptied: "Any mineral for which the He-3/He-4 ratio is conspicuously higher than for the surrounding minerals or area, is prime evidence that the host igneous or sedimentary formation was emplaced within the last few million years."⁴  That is a live young-earth argument and this site has not examined it.  It is not the atmospheric argument and it is not the zircon argument; it is a third thing, about ³He rather than ⁴He, and it deserves its own treatment rather than a wave of the hand here.

2005: Vardiman withdraws it at ICR

Seven years later the man who built the technical version dropped it, on his own organisation's website, in a survey chapter on evidence for a young earth from the ocean and atmosphere:

"Helium is a relatively light gas and a small amount can escape earth's gravitational field when it is ionized and accelerate upward by what is called the polar wind.  For several years before the magnitude of the polar wind was determined Vardiman (1990) reported that the lack of helium in the atmosphere argued for a young earth.  That argument is no longer valid based on the measured and computed escape rate of helium to space in the polar wind.  However, the large concentrations of helium remaining in crustal minerals is still a strong argument.  Humphreys (2005) has presented an air-tight case that the earth is 6,000 ± 2,000 years based on the residual concentration of helium in zircon grains of granites and the rapid diffusion rate of helium from them."⁵

Read exactly what he withdrew and exactly what he kept.  He withdrew the atmospheric argument, which is this article's subject, and he withdrew it for the reason given in the section above: the polar-wind escape rate stopped being a speculation and became a measurement.  He kept the zircon argument, which is a different claim about helium retained inside crystals, and he called it air-tight.  This site disagrees with him about the zircon argument, on separate grounds, at RATE and Helium in Zircons.  But the distinction he draws is the same distinction this article insists on at the top, and it would be dishonest to report the withdrawal as though he had given up more than he did.

Nobody made him do this.  The counter-apologetic literature had not engaged his paper: Matson cited the 1985 Impact pamphlet rather than the 1986 conference paper, and TalkOrigins' claims index cites Morris and does not mention Vardiman at all.  He changed his mind because a number was measured.  That is what should happen, and it is worth saying plainly on a site that spends most of its time grading arguments harshly.

The popular literature did not follow

Answers in Genesis was still running the argument in 2013, in chapter 10 of The New Answers Book 4:

"Another evidence of a young earth is the low amount of helium in the atmosphere.  The leakage rate of helium gas into the atmosphere has been measured.  Even though some helium escapes into outer space, the amount still present is not nearly enough if the earth is over 4.5 billion years old.  In fact, if we assume no helium was in the original atmosphere, all the helium would have accumulated in only 1.8 million years even from an evolutionary standpoint.  But when the catastrophic Flood upheaval is factored in, a flood which rapidly released huge amounts of helium into the atmosphere, it could have accumulated in only 6,000 years."²²

Three things about that passage.

It prints 1.8 million years in its own text, and footnotes the figure to Vardiman's 1990 monograph — the very work Vardiman named in 2005 when he said the argument was no longer valid.²²

The bridge from 1.8 million years to 6,000 is a Flood degassing pulse, and its footnote points to John Morris's The Young Earth, pp. 83–85.  Those are the pages where Morris says the opposite: that he suspects the helium was there at creation.  The popular argument is therefore resting on a page that undercuts it.

The chapter's "Rescuing Devices" subsection answers only zircon critics — helium diffusing in from surrounding minerals, mica "bottling" the crystals.  It offers no answer at all to ion escape, which is the objection that killed the atmospheric argument for Vardiman and for Brown.

Two more facts about where the argument stands in the movement.  Russell Humphreys' canonical list "Evidence for a Young World," fourteen items, contains "Too much helium in minerals" — the zircon argument — and contains no atmospheric-helium item at all.²³  Neither does Answers' "10 Best Evidences from Science That Confirm a Young Earth."  That is not a printed retraction, but it is a visible demotion, and it is the fairest available summary of the movement's current position: the technical people dropped the argument, the canonical lists dropped it, and one book chapter still prints it.

John Morris said the quiet part in 1994

The spine of this article is that the young-earth figure is an assumption rather than a measurement.  That is inferred above from Vardiman's technical paper.  It does not have to be inferred.  It is stated outright, in the movement's best-known popular book on the age of the earth, by the son of the man who made the argument famous.

John Morris gives the argument in The Young Earth with MacDonald's numbers converted to imperial units — "thirteen million helium atoms per square inch each second" of influx against "a maximum of about 0.3 million" of escape — and gets the same answer everyone gets: "Dividing the known amount of helium in the atmosphere by the rate of accumulation shows that all of the helium in the atmosphere today would have accumulated in no more than two million years!"⁶

Then he says what the two million years is worth:

"Please keep in mind, I don't conclude that the atmosphere is two million years old.  Instead, this teaches us that, using the uniformitarian assumptions inherent in every dating process, the atmosphere couldn't possibly be any older than two million years.  I'm convinced it's much younger."⁶

And then he says why he is convinced:

"This argument also assumes that at the time the atmosphere formed, there were absolutely no helium atoms present, and that all of the helium atoms there now have come about by this process.  But I suspect that at the time of Creation there were some helium atoms in the atmosphere, once again making the age much less.  Helium is a very useful, 'very good' element, and I suspect that the wise Creator would have included some in the original atmosphere."⁶

That is a leading young-earth author making the helium an initial condition, in print, in plain English.  The helium is young because the atmosphere is young, and the atmosphere is young because Scripture says so and because a wise Creator would have stocked it.  Those may be reasons for believing the earth is young.  They are not measurements of its age, and a quantity supplied by fiat at t = 0 cannot also be a clock.  Nothing in this article's Step one is an uncharitable reading of anybody;  it is what the movement's most-read popular book says on the page.

The movement has already retired one argument of exactly this form

Creation Ministries International maintains a page titled "Arguments we think creationists should NOT use."  Under "Which arguments should definitely not be used?" it lists moon dust:

"For a long time, creationists claimed that the dust layer on the moon was too thin if dust had truly been falling on it for billions of years.  They based this claim on early estimates—by evolutionists—of the influx of moon dust, and worries that the moon landers would sink into this dust layer.  But these early estimates were wrong, and by the time of the Apollo landings, NASA was not worried about sinking.  So the dust layer thickness can't be used as proof of a young moon (or of an old one either)."²⁴

Moon dust is structurally the identical argument.  Take an inventory, divide it by a present-day influx borrowed from mainstream sources, and call the quotient a maximum age.  It was dropped because the influx number turned out to be wrong.  The atmospheric-helium argument has the same shape, and the term that moved is the escape flux rather than the influx, but the consequence is the same: the quotient stopped meaning what it was said to mean.

The page's own standard is worth quoting back at it approvingly: "Persisting in using discredited arguments simply rebounds—it's the truth that sets us free (John 8:32)."  Neither CMI's list nor Answers in Genesis' equivalent has ever carried atmospheric helium.²⁴  The two people best placed to put it there put it in print somewhere else instead, in 1998 and 2005, where the popular writers did not see it.

Two young-earth arguments that this one contradicts

An argument can be wrong on its own and still be interesting.  What makes this one worth a long article is that it collides head-on with two other arguments the same movement promotes, and nobody in that movement appears to have noticed.

RATE's accelerated decay would drown the atmosphere in radiogenic helium

The RATE project's central proposal is that nuclear decay ran vastly faster during the Genesis Flood.  Their own statement of the budget is "about a half billion years of decay at today's rates," compressed into one year.²⁵  Most of that is alpha decay, and alpha decay makes helium-4.

Run the numbers.  At Torgersen's midpoint degassing rate, 500 million years of crustal production is 1.10 × 10⁴¹ helium-4 atoms.  At MacDonald's flux it is 1.61 × 10⁴¹.  The atmosphere holds 5.58 × 10³⁸.

So RATE's Flood-year pulse is 200 to 290 times the entire helium inventory of the present atmosphere.¹⁴

Vardiman's atmospheric model requires the crust to have supplied under 1% of the air's helium since creation, which is under 5.6 × 10³⁶ atoms.  The RATE pulse is about twenty thousand times that ceiling.  For both models to be true, under 0.005% of the RATE helium can have reached the atmosphere in the 4,500 years since.

And RATE's own physics says helium is mobile.  The whole point of their zircon work is that helium diffuses out of zircon fast enough that a 1.5-billion-year-old crystal could not have kept it.  Torgersen's paper says the continental degassing flux is approximately equivalent to whole-crustal production, meaning that over time essentially all of it does come out.  A model in which helium leaks briskly out of zircon at Fenton Hill but 99.995% of a two-hundred-atmosphere pulse stays locked in the crust everywhere else is not a model anyone has written down.

Larry Vardiman co-edited both RATE volumes.  The atmospheric argument is his, and the accelerated-decay proposal is the project he led.  These are not two rival camps failing to talk; they are one author holding both positions — until 2005, when he dropped the atmospheric one and kept the accelerated-decay one, which resolves the contradiction in the only direction it can be resolved.  The details of the zircon side are at RATE and Helium in Zircons, which reaches a negative verdict on independent grounds.

The popular version makes the collision explicit inside a single chapter.  Answers in Genesis' New Answers Book 4 bridges 1.8 million years down to 6,000 by "a flood which rapidly released huge amounts of helium into the atmosphere," four paragraphs after arguing that helium is still stuck in Precambrian zircons because it has not had time to leave.²²  A Flood pulse big enough to close a three-hundredfold gap is additive to RATE's accelerated-decay helium, and RATE's alone already overfills the atmosphere two hundred times.

And accelerated decay was never a settled young-earth position that this article is denying from outside.  In 1990 the Creation Research Society Quarterly ran an eleven-part "Minisymposium on Variable Constants," which its editor Don DeYoung introduced by saying that "this area desperately needs to be addressed."²⁶  Part X was R. H. Brown — the same man who repudiated the helium argument eight years later — arguing from the sharpness of radiohalo rings that "radioisotope half-lives over a range of 21 orders of magnitude have not varied by more than a factor of two" during the time the earth's geological formations have existed.²⁶  Part XI was Robert Gentry rejecting him in the next article: "The conclusion of the previous article (Brown, 1990) that the sharpness of halo rings established the constancy of radioactive decay rates is examined and rejected."²⁶  Gentry also stated the stakes for his own side more bluntly than any critic would:

"For example, if decay rates have remained constant, then creationists need to know it, for such a view firmly establishes the basis of conventional radiometric dating for fossils as well as rocks.  It appears that many creationists have thought all old radiometric ages associated with fossils can be explained away by contamination from prior radioactive decay."²⁶

John Byl, in part VII of the same symposium, granted the critics' central complaint: variable-constant proposals "appear at present to be strongly ad hoc," though he argued that is not by itself fatal.²⁶

So accelerated decay is not a fixed young-earth doctrine being attacked here from outside.  It was contested inside the Creation Research Society, in print, fifteen years before RATE published, and its own researchers could not agree whether the constants had varied at all.

And that leaves a young-earth writer with a choice, not an escape.  If decay rates have been constant, as Brown argued in 1990, then the air's helium is a few million years' worth of crustal production and the atmospheric argument fails on Brown's own 1998 arithmetic.  If decay rates were accelerated, as RATE argued in 2005, then the Flood year buried the crust in two hundred atmospheres' worth of helium and the argument fails the other way, because the air's helium can no longer be "almost completely primordial."  Which horn is live was argued head to head in one issue of CRSQ in December 1990, Brown on pp. 100–102 and Gentry on pp. 103–107, and it was not settled.

Humphreys' Flood reversals would scour the atmosphere clean

In 1972 W. R. Sheldon and J. W. Kern proposed that the dominant loss channel for atmospheric ⁴He is solar-wind ion pumping during geomagnetic reversals, when the dipole field passes near zero and the solar plasma reaches deep into the upper atmosphere.  Their abstract puts the shock penetration at about 700 km and the cascade ionisation rate above it at around 10⁹ ions cm⁻² s⁻¹, "sufficient to yield a secular equilibrium over geologic time scales."²⁷  Dalrymple's gloss, as Matson quotes him: "Sheldon and Kern [1972] estimated that 20 geomagnetic-field reversals over the past 3.5 million years would have assured a balance between helium production and loss."¹⁶

Creationists have treated this as an ad hoc rescue, and there is something to that.  It is a 1972 calculation that was never developed, the mainstream does not need it because the polar wind does the work, and the full paper is paywalled and was not read for this article.  But it was not invented to answer creationists.  MacDonald's own 1963 abstract already offered the general form of it, that "the rate of escape has varied in time," as one of the two ways out, before there was a creationist argument in existence to rescue anything from.

Now take the gloss at face value and see which way it cuts.  Twenty reversals balance 3.5 million years of production.  On the residence times above, 3.5 million years of production is about two atmospheres' worth of helium.  So each reversal episode removes roughly a tenth of the atmosphere's entire helium inventory.

Russell Humphreys' young-earth geomagnetic model puts the reversals inside the Flood year.  He sized his 1986 model for "roughly 50."  The documented polarity record contains about 185 reversals in the last 83 million years of the conventional timescale alone.²⁸  At a tenth of an inventory each, fifty reversals strip five atmospheres' worth of helium, and one hundred and eighty-five strip eighteen.  The atmosphere can only lose what it has, so the outcome is the same either way: an atmosphere scoured essentially clean of helium, 4,500 years ago.

And then the model has to put it all back.  Crustal degassing over 4,500 years supplies 0.18% of the present inventory.

A young-earth writer therefore has to choose.  He may say that helium cannot escape and reversal-driven escape is speculative.  He may say that hundreds of reversals happened in a single recent year.  He may not say both, because a published mechanism ties them together, and on that mechanism the second claim destroys the first.  The magnetic side of this is worked out at The Earth's Magnetic Field and the Age of the Earth.

Three flagship young-earth arguments, and at most one of them can be right.

Objections and responses

"The crustal degassing flux has never been measured.  It is an extrapolation from a handful of gas wells, and the whole argument turns on it."

This is correct, and Vardiman makes the point better than his critics do:

"Efforts to calculate the rate of flow of ⁴He from the crust to the atmosphere in other ways have met with very limited success.  First, it is difficult to measure the flow of such small quantities of a gas through an average crustal interface.  Secondly, the actual flow of helium seems to be concentrated in certain locations, such as near fumeroles, in volcanoes, at the mid-oceanic rise, etc.  The calculation of an average rate of flow based on non-homogenous time and space releases leads to large errors."²

He also identifies a real circularity in one of the two derivation routes: "the assumptions of no original helium and 4.5 billion year age of the earth are implicit in the conclusion that 6 × 10³⁸ ⁴He atoms entered the atmosphere at a rate of 2 × 10⁶ atoms/cm⁻²/sec⁻¹.  The same rate could have been calculated, assuming only 6 × 10³² ⁴He atoms entered the atmosphere over a period of 4,500 years."²

That objection lands against MacDonald's route and not against Torgersen's.  MacDonald's flux came from ⁴He/⁴⁰Ar ratios in natural gas combined with an assumed argon outgassing history, and Vardiman is right that an assumed age is buried in it.  Torgersen built his estimate from measured uranium and thorium concentrations in the crust and the resulting production rate, which does not need an age at all.  The two routes agree to within a factor of two, which is the reason to trust either.

But notice what the objection would have to deliver.  The residence time is inventory divided by flux, so to compress 1.76 million years into 6,000 the flux must be about three hundred times larger than published.  Morris took exactly that route, citing Henry Faul for an efflux "over 3 × 10¹¹ gms/year, which is about 100 times greater than the value used by Cook," and concluding "This in turn would reduce the age of the atmosphere down to several thousand years!"¹⁰  A hundredfold or three-hundredfold error in the crustal flux is not a matter of interpretation.  It is a claim that the crust contains a hundred times more uranium and thorium than measured, or degasses a hundred times more efficiently than any measurement shows.  Nobody has produced that measurement in the fifty years since.

"Non-thermal escape is a fudge.  It was invented because thermal escape did not work and the age of the earth had to be saved."

The timing does not support this.  Banks and Holzer worked out the polar wind from plasma physics, as an ambipolar diffusion problem in the high-latitude ionosphere; Axford applied it to helium in the same 1968 issue of JGR.  Neither paper is about the age of the earth.  And the mechanism was then observed rather than assumed: Kashyap records that polar-wind outflow "has been confirmed by observations made by several polar orbiting satellites," beginning with Explorer 31 in 1970 and ISIS 2 in the 1970s, and continuing with Akebono, POLAR and Dynamics Explorer 1 over altitudes from about 1,000 to 50,500 km.¹⁵  Her own outflow fluxes are taken from those observations, not fitted to close a budget.

Concede this much, though.  Sheldon and Kern's reversal mechanism does look like a rescue, it has not been developed since 1972, and the mainstream should stop citing it as though it were established.  And the global escape number is a model extrapolation from local satellite measurements, which is the same species of inference as the source flux.  Both sides of this budget are model-heavy.  That is the single most important thing to know about the whole dispute, and neither the creationist nor the counter-apologetic literature says it.

"You have conceded that escape is only 57% of the source.  If the budget really does not balance, why is that not a crisis?"

Because a missing factor of two in a globally averaged geophysical flux, where neither side is directly measured, is an ordinary state of affairs, and because the imbalance does not point anywhere useful.  Grant the whole residual and the answer is 6.6 million years, which is no closer to 6,000 than 4.5 billion is.  The gap is a research question about transport in the polar ionosphere and about how helium moves through 40 km of crust.  It is not a question about the age of the earth, because no plausible adjustment to either term produces a young answer.

What is fair to say is that the counter-apologetic literature has been sloppy.  "The escape of helium from the atmosphere balances its production" is stronger than the evidence supports, and the source cited for it is the source a later specialist criticised.  This site says so in the section above, and a skeptic who wants to hold the line on this topic should update his page rather than his conclusion.

"The ³He argument assumes the mantle reservoir composition you are trying to prove."

It does not, and this is worth taking slowly because it is the objection that would matter if it worked.

Every number in the mixing calculation is a measurement made on a physical sample, with no age assumed anywhere.  R_A is measured on air.  The 8 R_A value is measured on basalt glass dredged from mid-ocean ridges.  The 32 to 50 R_A values are measured on picrites and basalts from Loihi, Iceland and Baffin Island.  The 334 R_A solar value is measured on solar wind.  The 107 R_A planetary value is measured on gas trapped in meteorites.  The 0.02 R_A crustal value is what uranium and thorium decay produces in place, which is a nuclear-physics calculation with no free parameters.

The mixing arithmetic needs only one thing from all of that: that the primordial end-member sits above the atmospheric value.  Every measured candidate does, by factors between 8 and 334.  To break the argument you would need a primordial reservoir at or below 1 R_A, and there is no such reservoir on the books.  Postulating one is postulating a reservoir isotopically indistinguishable from the atmosphere itself, which assumes the conclusion.

There is also a direction argument that does not depend on picking an end-member at all.  ⁴He accumulates wherever uranium sits; ³He does not accumulate anywhere.  So any reservoir with uranium in it drifts downward in ³He/⁴He over time, and the longer it sits, the lower it goes.  The atmosphere is at the bottom of the entire measured range.  That is what a long radiogenic history predicts and what a freshly stocked primordial atmosphere does not.

The honest concession: the earth's initial helium isotope ratio is itself an inference, drawn from solar and meteoritic values rather than from a terrestrial sample.  A creationist is entitled to say that nobody has measured the composition of the atmosphere on day one.  What he cannot do is name a measured reservoir that would rescue the model.

"Chamberlain is the specialist and he said the problem is unsolved.  Why should a reader believe you over him?"

Read the next two sentences of his paragraph.  He names the polar wind and charge exchange, and the polar wind is the answer the field went on to adopt.  What Chamberlain said was unsolved is the quantitative budget, and it is still open to a factor of two, which this article states plainly.  He did not say that helium cannot escape, and he did not say the atmosphere is young.

"Maybe the escape rate was much higher in the past."

MacDonald raised this himself in 1963 as one of the two ways out.  It is a live possibility and it is not testable with present data.  Note, though, that it is an old-earth escape route, not a young-earth one.  It helps close a four-billion-year budget.  It does nothing for a 6,000-year one, where the problem is not too much helium but too little.

"You are only answering Vardiman.  Modern creationists do not use this argument much."

Half true, and the true half is more of a point in the movement's favour than the objection realises.  The technical creationist output on atmospheric helium stops in 1998, and it stops with a repudiation: Brown's Origins paper, followed by Vardiman's withdrawal at ICR in 2005.  So the two best-qualified young-earth authors on this subject are on the same side of it as this article.

The other half is not true.  The argument is still in print.  Answers in Genesis published it in a book chapter in 2013, eight years after Vardiman withdrew it, footnoting the 1.8-million-year figure to the very monograph Vardiman named when he said the argument was no longer valid.²²  A live claim in a book still sold is worth answering, and it is worth telling its readers that the argument's own technical authors have abandoned it.

This article answers the strongest published form because that is the fair thing to do.  It also answers it because the reasoning failure here is the same failure that shows up elsewhere: an assumed initial condition presented as a measured result.

Where the young-earth case is strongest

Not in the age, and not by a small margin.  It is strongest in a narrower place, and the place is real.

The mainstream budget does not close, and the confidence with which closure is asserted is not earned.  The counter-apologetic literature says the budget "balances."  On the best modern numbers escape is 57% of the source.  The escape side is computed from models whose cut-off-latitude assumption has been faulted in print by a later worker in the same field.  The source side has never been directly measured, and its canonical value comes from a paper whose abstract says the results "strongly suggest a steady-state He atmosphere" while conceding that the model requires ⁴He to be transported out of about 40 km of crust to work at all.²⁹

A creationist who says "the helium budget is not closed, the standard rebuttal rests on a paper another specialist says overestimates the polar cap, and the source flux is an inference rather than a measurement" is saying something true that most of his critics do not know.  He should say it.

A second point in his favour: the popular skeptical literature has never engaged the best version of the argument.  Matson cites the 1985 Impact pamphlet, not the 1986 conference paper.  CE001 cites Morris and not Vardiman.  Neither reply mentions that Vardiman computed the Jeans flux himself, or named the polar wind, or printed 1.76 million years.  Answering the weakest form and declaring victory is a failure mode this site tries to avoid, and the counter-apologetics has committed it here for thirty years.

A third, and it is the largest.  The best published critique of this argument was written by a young-earth author, in a young-earth journal, in 1998, and no counter-apologetic page cites it.  Brown got to the polar wind, to the 1.5-million-year fill time, to the insensitivity of that number to a tenfold cut in crustal production, and to the two-primordial-heliums problem, without any prompting from the skeptical side.  Creationist publishing produced that paper in 1998, and ICR withdrew the argument seven years later.  On this topic that side has corrected itself and its critics have not.

Where it fails

Morris's claim was false when he printed it.  "There is no evidence at all that Helium 4 either does, or can, escape from the exosphere in significant amounts" was written six years after Axford's paper and has been contradicted by direct satellite measurement of polar-wind ion outflow ever since.  Any presentation that still says this should be withdrawn.

The arithmetic never gives a young earth.  1.76 million years on Vardiman's own equation.  1.7 to 3.9 million years on the mainstream's own residence times.  6.55 million years on the residual imbalance.  0.24% of the inventory from 6,000 years of degassing.  There is no route from these numbers to thousands of years.

The young-earth figure is an assumption wearing a measurement's clothes.  Vardiman gets 10,000 years by supposing the helium was created in place, and he says so in print.  An assumed initial condition cannot date anything.  This is the single sentence that decides the argument, and it comes from the argument's own author.

And the assumption is falsified by the isotope ratio.  Air at 1 R_A requires 88% to 99.7% of its ⁴He to be crustal radiogenic.  Vardiman's model permits under 1%.  Cook named this as the decisive test in 1966 and again in 1986, and R. H. Brown ran it from inside the movement in 1998 and rejected the created-helium option on the same grounds.

And the movement's own experts have said so.  Brown in Origins in 1998: Jeans-escape modelling "does not provide significant evidence in support of (or contradictory to) a young-earth viewpoint."  Vardiman at ICR in 2005: "That argument is no longer valid based on the measured and computed escape rate of helium to space in the polar wind."  Neither was answering a critic.  Any presentation that still runs the argument is running it against its own authors.

Finally, the argument cannot coexist with two others the same movement promotes.  RATE's accelerated decay and Humphreys' Flood-year reversals each destroy it, from opposite directions.

Verdict

The anomaly is real.  The conclusion is not.

Melvin Cook asked a good question in 1957 and Gordon MacDonald sharpened it in 1963, and nothing since has made the question silly.  The atmosphere's helium inventory is a few million years' worth of the crustal source; thermal escape supplies 3% of what balance requires; the polar-wind answer, fifty-eight years on, still comes in at about 57% of the source with model uncertainties on both sides larger than the quoted error bars.  A skeptic who thinks this is a closed book has not read Kashyap.

But the young-earth conclusion never followed, and the reason is not a number.  It is a logical point that Larry Vardiman put in print himself.  His helium arithmetic gives 1.76 million years.  The 10,000-year figure comes from assuming the atmosphere was created with essentially all its helium already present.  Once that assumption is made the helium is an initial condition, and an initial condition cannot be a clock.  The argument that the atmosphere is young turns out to require, as a premise, that the atmosphere's helium says nothing about its age.

And the premise is testable.  Melvin Cook put the ³He/⁴He ratio on the table in 1966 and repeated it at the 1986 conference, Vardiman agreed in the same volume, and neither of them ran the calculation.  Run it and the air's helium is isotopically crustal, by 88% at the most generous and 99% at the most likely, where the model permits 1%.  The escape hatch is closed by a measurement, and R. H. Brown reached the same conclusion from the other side of the aisle in 1998.

And the people best placed to say so said it first.  R. H. Brown published the repudiation in a refereed young-earth journal in 1998, with the arithmetic, and named the polar wind as the mechanism.  Larry Vardiman, who wrote the technical version, withdrew it at the Institute for Creation Research in 2005 in one sentence: the argument "is no longer valid based on the measured and computed escape rate of helium to space in the polar wind."  He was not under pressure.  No critic had engaged his paper.  He changed his mind because a quantity was measured, which is the whole of what anyone should ask of an argument's author.

The most useful thing to take from this subject is not the verdict.  It is the shape of the failure, and of the correction.  Nobody lied, nobody faked a number, and the load-bearing arithmetic on both sides checks out.  An argument was raised honestly, answered in 1968, repeated for thirty years without anyone checking what the answer delivers, retired by its own side in 1998 and 2005 — and then printed again in 2013 by writers who had not read their own literature.  The creationists stopped at Jeans escape.  The skeptics stopped at Dalrymple.  The one man who read past both of them, Brown, is cited by neither.

What could not be read

This article names its gaps rather than hiding them, because a reader deserves to know which claims rest on bytes and which rest on someone else's summary.

• Axford 1968 and Banks and Holzer 1968, the two founding polar-wind papers, are paywalled at Wiley and printed no abstracts in that issue. Every route was tried and none worked. Their numbers appear above only as reported by Kashyap 2009 and by Vardiman 1986, and nothing is quoted from either paper.
• Vardiman's 1990 ICR technical monograph, The Age of the Earth's Atmosphere: A Study of the Helium Flux through the Atmosphere, could not be obtained. It is not among the 48 items archive.org holds from the Institute for Creation Research, ICR's own /i/pdf/technical/ directory carries only the 1986 conference reprint, and no library copy was reachable. Nothing is quoted from it. Its full title is fixed from Vardiman's own 2005 reference list.
• Vardiman's 1985 ICR Impact No. 143 has since been obtained and is quoted above. It is served by a 12 February 1998 Wayback capture of icr.org/pubs/imp/imp-143.htm; the 2008 capture of the same URL is a publications landing page with none of the article's text, and there is no imp-143.pdf.
• Cook 1957 beyond its first paragraph is paywalled. The first paragraph is served free by Nature and is quoted above; the rest of the letter is not. This matters less than it looks: Cook restates the whole argument at length on pp. 11–14 of Prehistory and Earth Models (1966), which is readable paragraph by paragraph, and that is where his own figures live.
• Dalrymple 1984, pages 112 and 113, is quoted here as Matson quotes it. The AAAS Pacific Division proceedings volume was not located and the page attribution is unverified.
• MacDonald 1963, Torgersen 1989, Sheldon and Kern 1972, and Lie-Svendsen and Rees 1996 are paywalled. Their abstracts were read verbatim and only their abstracts are quoted.
• Clarke, Beg and Craig 1969 and the Torr charge-exchange papers were not obtained. No number from either is claimed.
• Seven of the eleven CRSQ "Minisymposium on Variable Constants" papers were not read. Four were — DeYoung's editorial, Byl, Brown and Gentry — and only those four are cited. The unread seven are EPrints ids 691, 692, 697, 698, 703, 705 and 708 at crsq.creationresearch.org, all freely downloadable, and any of them could sharpen or complicate the paragraph above on accelerated decay.
• R. H. Brown's substitute argument is not answered here. His 1998 paper drops the atmospheric-helium argument and replaces it with a claim about excess ³He retained in minerals. That claim is quoted above and is not assessed anywhere on this site. Nothing in this article should be read as a reply to it.

Material that could not be verified at all is recorded in quarantine, not deleted.

Companion pages

• The literature — every source consulted, with what it measured, the access route that worked, and which way it cuts.
• RATE and Helium in Zircons — the other helium argument, on helium retained inside crystals rather than helium in the air.
• The Earth's Magnetic Field and the Age of the Earth — needed for the reversal mechanism, because the young-earth reversal model interacts with reversal-driven helium escape.

Sources