Gerald Schroeder's Six Days

Summary

Gerald Schroeder is an MIT-trained physicist who says the six days of Genesis 1 and the 13.8 billion years of cosmology are the same stretch of time, measured by two different clocks.  The claim is not that a "day" means an age.  It is that six literal twenty-four-hour days, ticked on a clock set by the cosmic microwave background near the beginning, arrive at Earth stretched by a factor of about four million million, and that the stretched interval is the age of the universe.

This article states his argument at full strength, in his own numbers, and then takes it apart.  The physics is the point of the exercise, not the theology.

• The core intuition is correct physics. Duration is frame-dependent. A process that takes twenty days at redshift 1 is observed to take forty days here. That is measured, in Type Ia supernova light curves and in quasar variability, and no serious cosmologist disputes it.¹ Schroeder did not invent this effect and does not misstate it.
• The application fails at the first step. Relativity compares the clocks of two observers who can be compared. Schroeder's "cosmic clock" is not a second observer. In the standard FLRW model every comoving observer, everywhere, shares one cosmic time, and their clocks all tick at the same rate. There is no clock in the universe that has ticked six days since the Big Bang. Creation Ministries International said this in 2000 and was right about it, even though it got Schroeder's mechanism badly wrong in the same paragraph.²
• (1 + z) is a cumulative record, not a rate. The factor of 4 × 10¹² is how much the universe has expanded since quark confinement. It is the total, integrated over 13.8 billion years. Using it as a fixed exchange rate between one second there and one second here treats a distance as a speed.
• His own equation does not close. Schroeder's formula on pages 68 and 69 of The Science of God halves the clock ratio once per Genesis day, starting from 4 × 10¹². Six halvings take 4 × 10¹² down to 6 × 10¹⁰, not to 1. At the end of the sixth day, on his own arithmetic, the cosmic clock is still running 60 billion times slower than Earth's. To get from 4 × 10¹² to 1 by halving takes 41.9 days, not six. This is not a rounding problem. The whole scheme requires the ratio to reach 1 exactly when Adam appears, and it does not.
• The halving series is fitted, not derived. Setting the half-life to exactly one Genesis day is the same as assuming the universe doubles in size once per Genesis day. It does not. On Schroeder's own timeline the universe expands by a factor of 2 × 10¹² during day one and by a factor of 1.02 during day six.
• The scheme contains at least five free choices: which epoch starts the clock, which temperature marks it, that the decay is exponential, that the half-life is one day, and that the clock switches to Earth time at Adam. Change the starting epoch from the proton threshold to the QCD transition and the calculated age drops from 15.5 to 2.5 billion years. Nothing in the model forbids that choice.
• A physically consistent version of the same idea gives the days in the opposite order. If the cosmic clock really ticks at the local microwave-background frequency, then a day defined by that clock is short early and long late, because the frequency falls as the universe expands. Integrating properly gives about four days total, with day one covering the first 60 million years and day six covering the last 5.8 billion. Schroeder's day one covers 8 billion years and his day six covers 250 million. The sequence is inverted. A reader on Sarah Salviander's site raised exactly this objection in 2014; the reply changed the definition rather than answering it.³
• The order of events does not match, and this is the strongest empirical test. Genesis has the Earth in verse 1 and the stars on day four. Cosmology has stars 9 billion years before the Earth. Genesis has fruit trees on day three, 3.8 billion years ago on Schroeder's timeline; there is no reliable flowering-plant fossil older than the Cretaceous, which begins about 143 million years ago. Genesis has winged creatures on day five and land animals on day six; the fossil record has land vertebrates by about 365 million years ago, the first winged insects at 325 million and the first bird at 150 million. Schroeder handles these by translating "fruit tree" as algae and "winged creature" as insect. Once translation is that free, the match is no longer evidence of anything.
• Genesis 1 says "evening and morning." That is a viewpoint on the surface of a rotating planet. Schroeder needs the viewpoint to be nowhere in particular. He answers by taking erev to mean "chaos" and boker to mean "order," which no Hebrew lexicon supports. Creation Ministries International's objection here is good and this article endorses it.⁴
• Sarah Salviander, an astrophysicist at the University of Texas at Austin, defends the model but reframes it. She locates the Genesis clock in "God's reference frame existing beyond space and time."⁵ That move rescues the theology and destroys the physics: a frame outside spacetime has no worldline, no proper time, and no relativistic relation to any clock inside. She also concedes, in a comment thread, that the viewpoint of Genesis 1 "does change to the surface of the earth later."⁵ If it does, the time dilation stops applying to days four through six.
• Creation Ministries International's published critique is a mixed bag and should be scored honestly. It is right that the day lengths are unmotivated, right that 15 billion divided by a million million is 5.475 days rather than 6, right that the million-million factor is taken from an arbitrarily chosen stage of expansion, right about the Hebrew, and right that Genesis 1:16 says the lights were made on day four. It is wrong that Schroeder "imagines an edge to the universe" and believes clocks near it run slow. He says the opposite in print: the effect is "not on changes in gravity, nor on differences in velocity," but on "the stretching of space."⁶ A creationist reading a caricature is still reading a caricature.
• What a better version would need. A defensible frame-based reading of Genesis 1 would have to name a physical worldline, derive the day boundaries from the expansion history rather than assume them, and predict the order of events rather than accommodate it. No such model exists. The one quantity that comes out of a correct calculation and lands near six is conformal time scaled to the microwave background at quark confinement, and it delivers the days backwards.

Where this site stands.  The Berean Archive holds a young-earth position, so Schroeder's proposal is not one it adopts.  That is a reason to be more careful here, not less.  An argument for a conclusion this site rejects still deserves an accurate statement, and an objection this site would like to be true still has to be correct.  Three of the published creationist objections to Schroeder are marked wrong below.

Who Gerald Schroeder is, and why the argument gets a hearing

Schroeder took his bachelor's, master's and doctorate at MIT, with a doctorate in two fields, earth sciences and physics, under the radiation physicist Robley D. Evans.  He stayed five years on the MIT physics staff, then moved to Israel, to the Weizmann Institute of Science and the Volcani Research Institute, with a laboratory at the Hebrew University.⁷  He is an Orthodox Jew, lives in Jerusalem, and reads Genesis in Hebrew.

None of that makes him right.  It does mean the argument is not a pamphlet.  Schroeder writes equations, cites Peebles' Principles of Physical Cosmology, and states his own error bar:  "I do not claim the ages I calculate are more accurate than plus/minus 20 percent."⁸  Critics who treat him as a naive concordist are attacking someone else.

Three books carry the argument.  Genesis and the Big Bang (Bantam, 1990) introduced it.  The Science of God (Free Press, 1997) contains the calculation, and is the book to argue with.  Every page number in this article is from the 2009 Free Press printing, which is the copy that was read.⁹  The Hidden Face of God (Free Press, 2001) restates it and, by his own account, covers it "in two chapters."⁶  A short essay, "The Age of the Universe," has been on his website for decades.  The version captured in May 2009 still counts the Jewish year as 5758, which is 1997-98, so the text goes back to about then;  the version on the site today has been revised.¹⁰

The rhetorical setup matters and should be stated fairly.  Schroeder restricts himself to Jewish commentary written before modern cosmology:  the Hebrew text, Onkelos (about 100 CE), the Talmud, Rashi (eleventh century), Maimonides (twelfth) and Nahmanides (thirteenth).  His reason is a good one.  "I refuse to use modern Biblical commentary, because modern commentary already knows modern science, and so it is influenced by that always."⁶  Whatever else is wrong with the argument, that constraint is a real attempt at intellectual hygiene, and it is more than most concordists impose on themselves.

He also insists, against nearly every other harmonizer, that the days are twenty-four hours.  He is not a day-age theorist in his own understanding of himself.  He points to Nahmanides as holding the days to twenty-four hours each while also holding that they contain kol yemot ha-olam, "all the ages and all the secrets of the world."⁶  The current version of the essay adds the Talmud at Hagigah 12A, Rashi there, and Nahmanides on Genesis 1:3 as the sources for the twenty-four-hour reading.¹⁰  The whole scheme is an attempt to make both halves of that sentence true at once.

The argument, at full strength

Here is the chain, in Schroeder's order.

One.  The Bible has two clocks.  The 5,758 years of the Jewish calendar are counted from Adam, not from the creation of the universe.  Schroeder's evidence is the liturgy and the Midrash, not physics:  Rosh Hashanah's Hayom harat olam commemorates the creation of the neshama, the human soul, and the Midrash at Vayikra Rabbah 29:1 has the sages agree that the six days sit outside that count.⁶  He reads Deuteronomy 32:7, "consider the days of old, the years of the many generations," with Nahmanides as a two-part calendar:  the six days, then everything after Adam.⁶

Two.  The biblical clock starts at quark confinement, not at the beginning.  Nahmanides writes misheyesh, yitfos bo zman, which Schroeder renders "from the moment that matter formed from this substance-less substance, time grabs hold."⁶  In the book the same phrase appears in the shorter form "when matter forms time grabs hold."⁸  Radiant energy, moving at c, experiences no proper time.  So the clock cannot start until stable matter exists.  Schroeder identifies that moment as the confinement of quarks into protons and neutrons, about 0.00001 second after the Big Bang, and identifies it with bohu in Genesis 1:2, which he and the Talmud read as "filled with the building blocks of matter" rather than "void."⁸

Three.  The cosmic microwave background is the clock.  It fills the whole universe, it is not tied to any location, and it has been present since the beginning.  Its frequency is the tick rate.  Schroeder quotes the standard fact that "the directly measurable coordinate along the line of sight is not time, but redshift."⁸

Four.  The stretch factor is about a million million.  The threshold temperature of protons is 10.9 × 10¹² K.  Today's microwave background is 2.73 K.  The ratio is 4 × 10¹², which Schroeder calls "a million million."  Light emitted then and received now has been stretched by that factor, and so, he argues, has the perceived interval between events:  "That cosmic timepiece, as observed today, ticks a million million times more slowly than at its inception."⁸

Five.  Six days become fifteen billion years.  "In terms of days and years and millennia, this stretching of the cosmic perception of time by a factor of a million million, the division of fifteen billion years by a million million reduces those fifteen billion years to six days!"⁸  And then the line the argument is famous for:  "When one asks if six days or fifteen billion years passed before the appearance of humankind, the correct answer is 'yes.'"⁸

Six.  The days are not equal, and they halve.  Each doubling of the universe halves the cosmic clock rate.  Doubling takes longer as the universe grows.  So each successive Genesis day covers half the Earth time of the one before.

That is his table from page 63, transcribed.⁸

Seven.  The events line up.  Schroeder then puts each day's biblical content beside the scientific record and says the fit is the real test:  "The Bible not only tells us that six days passed between the creation of the universe and the creation of Adam, but it also records the key events that occurred on each of those days."⁸  On his website he is blunter:  "They match up close enough to send chills up your spine."⁶

His day-by-day table, from page 70, runs:  day one, the Big Bang, light breaking free at recombination, first galaxies;  day two, the Milky Way's disk and the Sun;  day three, oceans and the first life at 3.8 billion years;  day four, the atmosphere turning transparent so the Sun, Moon and stars become visible;  day five, the Cambrian explosion and winged insects;  day six, the end-Permian extinction, then land animals, mammals and humankind.⁸

Where the numbers actually come from

Most summaries of Schroeder stop at "a million million."  The book contains an equation, and the equation is where the argument can be checked.  It is on pages 68 and 69.

He uses the exponential decay formula, the same one that describes radioactivity:

A = A0 e^(-Lt)

• A is Earth time: "the number of current Earth days contained within one Genesis day at any given instant."
• A0 is the ratio of the microwave background temperature at quark confinement, 10.9 × 10¹² K, to today's, 2.73 K. That is 3.99 × 10¹².
• L is "the natural log of 2 (usually written ln 2, and equals 0.693) divided by the half period." And then the sentence that decides everything: "The half period is one Genesis day."⁸
• t runs from zero to six, in Genesis days.

Integrate that over each day and the table falls out.  Day one is A0(1 − ½)/ln 2 = 2.88 × 10¹² Earth days, which is 7.89 billion years.  Every following day is half the one before.  Adding the six gives 15.5 billion years.  Schroeder reports 15.75, which is what you get by integrating to infinity rather than stopping at six, and it is also what you get by adding his own rounded entries:  8 + 4 + 2 + 1 + ½ + ¼.  He then says:  "The sum of the durations of all six days is a prediction of the age of the universe.  This calculated age of the universe equals 15.75 billion years."⁸

Three things follow immediately, and they are the whole case.

A0 is a choice.  10.9 × 10¹² K is the temperature whose thermal energy equals the proton's rest mass, 938 MeV.  It is not the temperature of the quark-hadron transition, which lattice QCD puts at 154 ± 9 MeV, or 1.8 × 10¹² K.¹¹  Pick the QCD transition instead and A0 falls by a factor of six, and the calculated age of the universe falls from 15.5 billion years to 2.5 billion.  Pick recombination and it collapses to nothing.  Pick the Planck time and it explodes.  The answer is not robust against the one input the model does not derive.

L is a choice too, and a stranger one.  Setting the half period to one Genesis day says the universe doubles in size exactly once per Genesis day.  Schroeder states the physics correctly on the page before:  "Each doubling in size 'slowed' the cosmic clock by a factor of 2."⁸  But the universe has doubled about 42 times since quark confinement, because log₂(3.99 × 10¹²) = 41.9.  Six doublings is not 42 doublings.  On Schroeder's own timeline the universe expands by a factor of 2 × 10¹² during day one and by a factor of 1.02 during day six.  Neither is 2.

And the equation does not land on the present.  At t = 6 the formula gives A = A0/64 = 6.2 × 10¹⁰.  That says one Genesis day at the end of day six still equals 62 billion Earth days, about 170 million years, and it says the cosmic clock is still running 6 × 10¹⁰ times slower than a clock on Earth.  But Schroeder identifies that ratio with the redshift factor, and a redshift factor of 6 × 10¹⁰ means a microwave background temperature of 1.7 × 10¹¹ K, which is about 15 MeV, which is roughly three milliseconds after the Big Bang.  So his equation places the end of the sixth day both at Adam and at three milliseconds.  Both readings come from the same formula and the same identification, and they cannot both be right.

Schroeder later moved the numbers, and the way he moved them is instructive.  His current website essay reports the ages as 7.1, 3.6, 1.8, 0.89, 0.45 and 0.23 billion years, totalling 14.07.  The change came from a correction he says was pointed out after a talk at Azusa Pacific University in February 2011:  that he had not allowed for accelerating expansion, and that had the expansion been linear "the CMRB would be, not the currently observed 2.76 K, but 3.03 K."¹⁰  Substituting 3.03 for 2.73 in the denominator of A0 lowers the whole series by ten percent, and every one of his six new numbers is reproduced exactly by doing that.  But the microwave background temperature is a measurement, 2.72548 ± 0.00057 K.¹²  Replacing a measured quantity with a hypothetical one because the output needs to move ten percent is fitting, not correcting.  The model's answer has tracked the published age of the universe from 16 billion to 15.75 to 14, which is what an accommodating model does and what a predictive one does not.

The popular version of the argument does not even agree with the technical one.  On his website Schroeder multiplies five and a half days by a million million, divides by 365, and reports "14 billion years."¹⁰  That multiplication actually gives 15.07 billion years.  Creation Ministries International caught the same slip in the older version, where six days times a million million was called the age of the universe:  the product is 16.4 billion years, and fifteen billion years divided by a million million is 5.475 days, not six.⁴  Those are small errors on their own.  They matter because the argument's entire rhetorical force is that two independent numbers coincide, and a coincidence that needs rounding at every step is not much of a coincidence.

The physics

What relativity actually lets you compare

Relativity does not say time is subjective.  It says that the interval between two events depends on the path taken between them, and that two observers who follow different paths and then meet again can find different amounts of elapsed time on their watches.  The twin who flies away and comes back really is younger.  This is measured, in flying atomic clocks, in GPS satellites, and in the decay lifetimes of fast-moving muons.

The comparison requires two things.  There must be two worldlines, meaning two actual paths through spacetime that something could follow.  And there must be a way to relate them:  they meet, or one sends light to the other, or they sit at fixed positions in a shared gravitational field.  Without both, "whose clock runs slower" has no answer, because there is nothing to compare.

Schroeder's cosmic clock has neither.  He says so himself, and says it as though it were a strength:  "The Bible's clock before Adam is not a clock tied to any one location."⁸  A clock not tied to any location is not a clock.  It has no worldline, so it has no proper time, so there is nothing for relativity to relate to a clock on Earth.

Sarah Salviander makes the same move and makes it explicit.  Asked to say where the Genesis clock sits, she lists three things it depends on, and the first is "God's reference frame existing beyond space and time, which regards the universe as a whole."⁵  As theology that may be unobjectionable.  As physics it ends the argument, because a frame outside spacetime has no metric, no light cone, and no time dilation factor with respect to anything inside.  You cannot run a Lorentz transformation between a coordinate system and eternity.

Cosmic time exists, and it is exactly the wrong thing for the argument

Here is the part that is genuinely surprising, and it cuts against Schroeder rather than for him.

General relativity has no universally preferred frame.  But the standard cosmological model is not general relativity in general.  It is the Friedmann-Lemaître-Robertson-Walker solution, which assumes the universe is homogeneous and isotropic, and that assumption does single out a preferred slicing.  Peebles describes the construction:  "In this construction one imagines a set of observers, each equipped with a clock synchronized relative to the neighboring observers, and each comoving with the mean motion of the material averaged over a neighborhood large enough to remove the local fluctuations away from homogeneity."  The reading on that observer's clock is the coordinate t, which he calls world time, and "Homogeneity and isotropy require that the mean mass density and pressure are functions only of this world time t."¹³

So there is a cosmic clock.  Every galaxy carries one.  They are all synchronized, and they all read the same thing:  about 13.8 billion years.¹⁴  That is what the number means.  It is not "13.8 billion years as measured from Earth, and something else elsewhere."  It is the proper time along the worldline of any observer at rest with respect to the mean matter distribution, which includes Earth to a very good approximation.

Creation Ministries International stated this in August 2000, in one sentence, correctly:  standard Big Bang theory "has all its clocks running at the same rate everywhere."²  They were right.  The universe already has the privileged frame Schroeder needs, and it does not do what he needs it to do.  No comoving clock anywhere has ticked six days.  They have all ticked 13.8 billion years.

(1 + z) is a total, not a rate

Schroeder's conversion factor is the redshift of the microwave background between quark confinement and now.  He quotes Peebles for it, and the quotation is real.  On page 96 of Principles of Physical Cosmology, after giving the relation between emitted and observed frequencies, Peebles writes:  "This also applies to proper rates of events, as one sees by the same application of a sequence of Lorentz time-dilation factors."¹³  Schroeder reproduces the sentence with the comma and the word "same" dropped, which changes nothing.⁸

What it applies to is the point.  Read the paragraph it sits in and the subject is unambiguous:  a source emits radiation at frequency ν_e, an observer receives it at ν₀, and the ratio is a₀/a_e.  Peebles' sentence extends that from wave frequency to any repeating process at the source.  A supernova at z = 1 is observed to fade over forty days instead of twenty.  That is a statement about signals in transit.  It is not a statement that the supernova took forty days.

The distinction is everything.  (1 + z) is not a rate at which one clock runs against another.  It is the accumulated stretch of a wave that has been travelling for billions of years.  It grows as the light travels.  Using 4 × 10¹², the value accumulated over the whole history of the universe, as a fixed exchange rate between one second at the beginning and one second now is like reading a car's odometer and calling it the speedometer.

There is a way to see how badly this goes wrong.  Take Schroeder's own picture:  an intelligent community at quark confinement flashes a light once a second, and we receive the flashes 10¹² seconds apart.⁶  Fine.  Now ask how long that community can go on flashing.  Quark confinement is 10^-5 seconds after the beginning.  Six days later the universe is six days old, and the radiation-era temperature has fallen to roughly 10⁷ K, so the stretch factor for light emitted at that moment is of order 10⁶ to 10⁷, not 4 × 10¹².  Six days of their signals therefore arrive spread over of order a hundred thousand years, not fifteen billion.  The factor is not a constant, and it is not even approximately constant over the interval Schroeder needs.

Schroeder knows the factor is not constant, which is why he lets it decay.  But the decay he uses is an exponential in Genesis-day number with a half-life he assigns.  The decay the universe actually has is set by the expansion history.  Those are different functions, and substituting one for the other is where the argument is lost.

The same idea, done consistently, gives the days backwards

Take Schroeder seriously and build the clock properly.  Let the cosmic clock tick at the local microwave background frequency, which is what he says it does.  That frequency falls as 1/a, where a is the scale factor.  So the elapsed reading on that clock between the beginning and now is

tau = (a_bohu / a_0) * INTEGRAL from 0 to t0 of (a_0 / a) dt

That integral is conformal time.  For the Planck 2018 parameters, Ω_m = 0.315, Ω_Λ = 0.685, H₀ = 67.4 km/s/Mpc, it comes to 46.1 billion years.¹⁵  With a_bohu/a₀ = 2.7255/(1.089 × 10¹³) = 2.50 × 10^-13, the cosmic clock has ticked off

4.2 days.

That is a striking number and this article will not pretend otherwise.  A physically defensible construction, using Schroeder's own choice of starting epoch and no fitted parameters at all, lands within a factor of one and a half of six days.  Nudge the starting epoch to 660 MeV instead of the proton mass and it lands on six days exactly.  Something about the order of magnitude is real, and the reason is not mysterious:  the comoving horizon in units of the earliest reasonable clock tick is a number of that size, and it is a number a physicist should find interesting.

And then the construction destroys the argument, because it delivers the days in the wrong order.  Split those 4.2 days into six equal parts and read off where the boundaries fall in cosmic time:

The days get longer, because the clock ticks fastest when the universe is smallest.¹⁵  Schroeder's days get shorter.  His day one holds 51 percent of cosmic history;  a consistent calculation puts 0.6 percent there and 44 percent in day six.

This is not a subtle objection and it did not need this article to find it.  A reader wrote to Salviander in July 2014 with exactly this point:  "the Genesis days measured in Earth time should be getting progressively longer, not shorter (7 billion years, 3.5 billion years, 1.8 billion years, …)."³  Her reply is that "this person is mistakenly assuming that the number of cycles in a Genesis day is fixed."³  But a clock is a fixed number of cycles.  That is what a clock is.  The second is defined as 9,192,631,770 cycles of a caesium transition.  If the number of cycles per Genesis day is allowed to float, the microwave background is not being used as a clock at all, and the argument has lost the only thing that made it quantitative.

Evening and morning

Genesis 1 says, six times, "there was evening and there was morning."  Evening and morning are what a rotating planet's surface does with respect to a nearby star.  They are not features of the universe as a whole, and they are certainly not features of a frame "beyond space and time."  If the vantage point of Genesis 1 is nowhere in particular, the text's own time markers are unintelligible.

Schroeder sees the problem and answers it by re-etymologizing.  Following Nahmanides, he takes erev to mean not evening but chaos:  "the Hebrew letters Ayin, Resh, Bet ... is chaos.  Mixture, disorder."  And boker, morning, becomes bikoret, order:  "from erev to boker is a flow from disorder to order, from chaos to cosmos."⁶

Creation Ministries International's objection here is correct and this article endorses it without qualification.  The Hebrew for chaos in Genesis 1:2 is tohu, which shares no root with erev;  the standard word in the ordering semantic field is seder, which shares no root with boker.⁴  Erev means evening, and it is used that way hundreds of times, including in Genesis 1 itself, where the same word carries the ordinary sense in the phrase that closes each day.  Even granting the root-meaning move, it proves too much:  every day would have to begin in chaos and end in order, and the account would be six repeated cycles of collapse and recovery, which is not the story Genesis tells.

The deeper problem is structural.  Schroeder needs Genesis 1 to be told from a viewpoint outside the Earth, because that is the only place his clock can sit.  But the text's own vocabulary is terrestrial from verse 2 onward:  a surface, waters, dry land, lights "in the expanse of the heavens" that serve "for signs and for seasons," birds flying "across the expanse."  Signs and seasons are for someone standing on the ground.

Salviander was pressed on this and conceded it.  A commenter argued that "the point of view from Genesis 1:2 onward is the earth's surface, not the edge of space-time," and she answered:  "Yes, the point of view does change to the surface of the earth later in Genesis 1."⁵  The next commenter drew the obvious consequence:  if the viewpoint has moved to Earth by day four, "then there is no time dilation for days 4, 5, 6 and 7.  His model then fails."⁵  That is right.  Schroeder's own table needs days four, five and six to hold 1.75 billion Earth years between them. If the narrator is standing on the ground from verse 2 onward, those 1.75 billion years have nowhere left to sit.

A privileged frame does exist, and it is measured every day

One more point deserves stating plainly, because both sides of this argument usually get it wrong.

Popular writing says relativity forbids a preferred frame.  That is true of special relativity and of general relativity as a theory.  It is not true of the universe we live in.  The matter in the universe defines a rest frame, and that frame is measurable.  The microwave background is not isotropic;  it has a dipole, hotter in one direction and colder in the opposite one, with an amplitude of 3362.08 ± 0.99 µK.  Read as a Doppler shift, that says the Sun is moving at 369.82 ± 0.11 km/s toward a point in the constellation Crater.¹⁶  Planck then checked the reading by a completely different method, the aberration and modulation of the small-scale pattern, and got 384 ± 78 ± 115 km/s in the same direction.¹⁷

So the "cosmic clock" Schroeder wants is not a philosophical posit.  It is a physical frame, we know our velocity with respect to it to a tenth of a kilometre per second, and Earth is very nearly at rest in it.  A clock at rest in that frame is the clock that reads 13.797 ± 0.023 billion years.¹⁴  Schroeder's argument needs the universe to lack the frame that the universe in fact has.

The halving series is fitted, and here is the count

The exponential in Schroeder's equation is where the six days come from.  It is worth asking whether anything derives it.

Nothing does.  The formula has two inputs, A₀ and L, and each is set by hand.

Free choice one:  which event starts the clock.  Schroeder starts it at quark confinement, on the theological ground that time cannot run before stable matter exists.⁸  That is an argument from Nahmanides, not from physics.

Free choice two:  which temperature marks that event.  He uses 10.9 × 10¹² K, the temperature whose thermal energy equals the proton's rest mass.  The lattice-QCD number for the actual transition is 154 ± 9 MeV, six times lower.¹¹  The output is proportional to this input, so a six-fold change in the input is a six-fold change in the age of the universe.

Free choice three:  that the ratio decays exponentially in Genesis-day number.  The real clock ratio is (1 + z), which is a function of cosmic time set by the Friedmann equations.  It is not an exponential in day number, and Schroeder gives no derivation connecting the two.

Free choice four:  that the half period is one Genesis day.  This is the sentence that produces the answer.⁸  It says the universe doubles in size once per Genesis day.  Schroeder himself states the correct physics on the page before, that each doubling halves the cosmic clock rate,⁸ and the universe has doubled about 42 times since quark confinement.¹⁵  Six is not 42.

Free choice five:  that the cosmic clock stops and Earth time starts at Adam.  In The Science of God the switch happens at the creation of Adam, and the footnote to the day table says the exact integration terminates the cosmic view of time there rather than at the end of day six.⁸  On the website the same switch is stated flatly:  "The Talmud tells us that the soul of Adam was created at five and a half days after the beginning of the six days.  That is a half day before the termination of the sixth day.  At that moment the cosmic calendar ceases and an earth based calendar starts."¹⁰  Nothing in the physics knows about Adam.

There is now a sixth, added in 2011.  The current website version replaces the measured microwave background temperature with a hypothetical one, 3.03 K instead of 2.76 K, on the ground that the expansion has not been linear.¹⁰  That lowers every day length by ten percent and moves the total from 15.75 to 14.07 billion years, which is where the published age of the universe had moved.

Count them.  A model with five or six adjustable inputs, fitted to reproduce one number, has not predicted that number.  Creation Ministries International said the same thing about A₀ in 2000, and on this point they were right:  the million-million figure "is an order of magnitude number taken from an arbitrarily chosen stage of expansion in the alleged big bang.  Another person could just have well taken a number a thousand times bigger, or a thousand times smaller."²

And there is a cleaner way to see that the series is fitted rather than found.  Ask what the boundaries between Genesis days would have to be if the microwave background really were the clock.  Equal intervals on that clock are equal intervals of conformal time, and that calculation was done above.  It gives days that grow, not days that halve.  Schroeder's halving series is not what his own choice of clock produces.  It is what produces his answer.

Two Christian astronomers, and they contradict each other

Schroeder's model is often framed as science against religion.  It is not.  The sharpest disagreement about it is between two credentialed Christian astronomers who reach opposite conclusions from the same relativity.

Sarah Salviander did her graduate work in astrophysics at the University of Texas at Austin¹⁸ and describes distant quasars as her own research field.⁵  She is an old-earth creationist.  She puts Homo sapiens at about 200,000 years and the Cambrian explosion at about 500 million, and holds that hominids preceded Adam and lacked the neshama, the human soul, following Maimonides and Nahmanides through Schroeder.¹⁹  Asked why so many Christians insist on a young universe, she answers:  "I am still trying to figure that out."¹⁹  She calls Schroeder's model "a scientifically sound model" and says he reconciles six 24-hour days with billions of years "convincingly."⁵  She adds that the same redshift correction is one "I have to take into account in my own research on distant quasars."⁵

Jason Lisle has a PhD in astrophysics from the University of Colorado and is a young-earth creationist.²⁰  He rejects the model.  His engagement with it is one paragraph long and it is the only place in 220 posts on his site where he mentions Schroeder at all.²¹  He gets the name wrong, calls him "Gerard Schroeder," and cites the 1990 book rather than the 1997 one, so he is arguing with the popular version.²¹  His two objections are still the right two.

Lisle's first objection is the reference frame.  "One fatal problem with this view is that Genesis gives the timescale from the perspective of Earth – not from distant galaxies.  Each of the days is defined in terms of one morning and one evening;  in other words, the days of creation are based on the rotation of Earth.  And the ages of the patriarchs are Earth-years.  So, biblically, the timescale of about 6000 years is from our perspective."²¹

That is the same premise Lisle uses to justify his own anisotropic synchrony convention, which reads Genesis 1 as timestamped at the Earth's surface.²⁰  Schroeder and Salviander need the opposite premise, that Genesis 1 is narrated from outside the universe.  Neither side can prove its premise from physics, because the question is what the text is doing.  The whole dispute between these two camps reduces to one exegetical question, and Salviander conceded half of it in her own comment thread when she agreed the viewpoint moves to the Earth's surface later in the chapter.⁵

Lisle's second objection is the order of events, and time dilation cannot touch it.  "According to the Bible, the Earth is there at the beginning (day 1), but stars are made on day 4 (Genesis 1:14-19).  But in the big bang view the stars were around billions of years before the Earth.  In the secular timescale, fish existed long before fruit trees, but the Bible has fruit trees being made on day 3, whereas fish are made on day 5.  Claiming that the days were long from one perspective, or that there are gaps in between will not resolve these problems."²¹

He is right about the logic.  Any change of clock is a monotonic reparameterisation of time.  It can stretch an interval or squeeze it.  It cannot swap two events.  If the record says A came before B and the text says B came before A, no clock anywhere in the universe fixes that.

Two things follow, and neither is comfortable for anyone.  Lisle's objection would also apply to a young-earth reader who accepted the fossil sequence, so it is not a free hit.  And the two men have never engaged each other:  a full-text search of all 220 posts on Lisle's site and all 371 on Salviander's finds no mention of either by the other.²²  Two Christian astronomers, twenty years, one shared subject, no conversation.

The order of events

This is the strongest test, and it is the one Schroeder himself proposed.  "The Bible not only tells us that six days passed between the creation of the universe and the creation of Adam, but it also records the key events that occurred on each of those days."⁸  He then invites the comparison:  "let's compare day by day the fidelity by which the events of Genesis map onto the corresponding discoveries of science."⁸

Here is that comparison, with the dates the model assigns and the dates the record gives.

Two of these are genuine hits and this article will not pretend otherwise.  Light released well after the beginning is right, and it is a strange thing for an ancient text to have.  Water and early life arriving close together is roughly right, and it was not the expected answer when Schroeder wrote.  He says so himself, and the claim that life appeared immediately after liquid water was new and contested then.⁸  It is still at the early end of a contested range, so it should be counted as a soft hit, not a hard one.

The four failures are of a different kind.  They are not near misses.  Genesis puts the Earth before the stars and the model puts the stars nine billion years before the Earth.  Genesis puts fruit trees on day three and the record puts flowering plants 3.6 billion years later.  Genesis puts winged creatures before land animals and the record puts land vertebrates 40 million years before the first winged insect and 215 million years before the first bird.  Genesis makes the sun on day four, after plants, and the model needs the sun on day two.

Schroeder's answer in every case is translation.  "Fruit tree" becomes bacteria and photosynthetic algae, with Kabbalah cited for the claim that day three "marked only the start of plant life."⁸  "Winged creature" becomes winged insect.  The sun being "made" on day four becomes the sun becoming visible on day four, which requires Genesis 1:16 to mean "appeared" when it says "made."  Creation Ministries International's objection to that last move is correct:  Hebrew has a word for "appear," and Genesis 1:16 does not use it.⁴

The deeper problem is that once translation is that free, the fit is no longer evidence.  A day-by-day match is impressive only if the matching rule was fixed before the comparison.  Here the rule is chosen per day, to make each day match.  Schroeder is honest enough to show his working, which is what makes the point visible;  many concordists hide it.

Scoring the creation.com critique

Creation Ministries International published a two-part review in August 2000, drawing on contributions from D. Russell Humphreys and Ron Samec.⁴²  It is the most-cited creationist response to Schroeder.  It is a mixed document and a reader on this site deserves to be told which half is which.

Right, and worth repeating.

• The day lengths have no derivation. "He does not rest this choice of variable 'day' lengths on any discernible scientific reasoning, nor does he offer any biblical basis for such a division."⁴ That is exactly the free-choice problem above.
• The arithmetic does not close. Fifteen billion years divided by a million million is 5.475 days.⁴
• The starting ratio is arbitrary. It is "taken from an arbitrarily chosen stage of expansion."²
• The Hebrew is wrong. Erev has no root relation to tohu, and boker none to seder.⁴
• Genesis 1:16 says the lights were "made," not that they appeared.⁴
• The chaos-to-order reading proves too much. If erev to boker is disorder to order, every day repeats the cycle. "Did things go through a six 'day' cycle of chaos-to-order-to-chaos-to-order?"⁴
• Standard cosmology has no differential clock rates to exploit. Big bang theory "has all its clocks running at the same rate everywhere."²

Wrong, and this site does not endorse it.

• The edge. "Not realizing that the big bang theory has no 'edge' to its matter, Schroeder imagines such an edge and appears to believe that clocks near such an edge run slow compared to clocks on Earth."² Schroeder says the opposite in print. His effect is "not on changes in gravity, nor on differences in velocity," but on the stretching of space.⁶ Salviander states the same thing and adds that "there is no edge of spacetime."⁵ The review is arguing with a position Schroeder does not hold, and the sentence immediately after it, about clocks running at the same rate everywhere, is both correct and a better objection.
• The day-age charge. The review calls the model "nothing more than a new variation on the tired old 'day-age' theory."⁴ Schroeder holds the days to twenty-four hours in the frame he specifies. He is wrong about the frame, but he is not saying a day means an age, and the difference matters because it is the whole reason his scheme has an equation in it.
• The theological argument. Part 2 says that accepting the model "takes away death as a penalty for sin, clearly taught by Genesis 2:17 and 3:19, and nullifies the work of Jesus on the cross."² Whatever its merits as theology, it is not an argument that the physics is wrong, and the review presents it among the physics.

Half right.  The review notes that Schroeder's number tracked the published age of the universe and no longer fits:  "According to his theory, to get 6 days you need a 16 or 17 billion-year-old universe."²  The observation is fair and the article above makes a stronger version of it, since Schroeder later moved the input rather than the output.  But the review's own recalculation, that we are "in day 4.8 instead of 5.5," treats the model as if the day boundaries were fixed, which they are not.

What a better version would have to look like

Three things would have to be true, and none of them is true now.

One:  name a worldline.  A relativistic argument compares two clocks.  Each clock has to sit on something that could carry a clock, meaning a particle, an observer, or a comoving point.  "The universe as a whole" is not one, and "God's frame beyond space and time" is not one either.  Until the Genesis clock is attached to a worldline, there is nothing for a time-dilation factor to be a factor between.

Two:  derive the day boundaries.  A model that assigns six intervals must say what makes a boundary.  Schroeder's boundaries come from setting a half-life equal to a day, which is circular.  A non-circular version would take the expansion history and produce the boundaries, and the honest version of that calculation is in this article:  it gives six intervals that grow, with day one covering the first 76 million years and day six covering the last 6 billion.  That is a real result and it contradicts the text more sharply than Schroeder's version does.  Genesis has almost everything happening late.  A conformal-time reading has almost everything happening late in cosmic time, which is the same direction, but the biblical content of the early days is cosmological and the content of the late days is biological, and the conformal reading puts galaxy formation in day two and the Cambrian in day five, which is not much of an improvement.

Three:  predict the order.  This is the test the model cannot pass by adjustment, and it is the one Schroeder chose himself.  A better version would have to say, before looking, which events fall in which day, and then be checked.  The current version reads the record first and then supplies the translation each day needs.

There is one thing in the neighbourhood that is genuinely interesting, and this article would rather state it than bury it.  The comoving horizon of the universe, measured in ticks of a clock set to the microwave background at the temperature of the proton mass, is about four days.  Move the starting temperature to 660 MeV and it is six days exactly.¹⁵  That number falls out of standard cosmology with no fitted parameters.  It means nothing on its own, because there is no observer whose clock reads it, and because the resulting days run backwards against Genesis.  But it is not nothing, and the reason Schroeder's argument has persuaded intelligent people for thirty years is that a number of this size really is sitting there in the equations.

Where this leaves the young-earth reader.  Nowhere better off.  Schroeder's model is not a young-earth model and its failure is not a young-earth argument.  The one part of it that this site would want to be true, that six ordinary days and a long cosmic history can both be literally correct, is the part that fails hardest, because it needs a frame that the standard cosmology does not have and that the microwave-background dipole rules out.

Objections and responses

"You have not read Schroeder;  you are attacking a caricature."  Salviander makes this charge against his critics and it is often deserved.⁵  Every number in this article comes from The Science of God or from Schroeder's own website, with the page or paragraph given.  His equation is quoted with its own definitions of A, A₀, L and t, and the arithmetic is carried out on his inputs rather than on substitutes.  Where creationist critics have misstated him, this article says so and names the misstatement.

"Time dilation is real, so the mechanism is real."  Time dilation is real and Schroeder does not misstate it.  Distant supernovae fade in (1 + z) times longer than nearby ones, and quasar variability shows the same stretch.¹  What is at issue is whether that effect gives a ratio between one second at the beginning and one second now, for two clocks that both exist.  It does not.  It gives the accumulated stretch of a signal in transit, and that stretch is a growing function of travel time, not a constant.

"God's perspective is outside time, so relativity does not have to apply."  Then neither does the calculation.  The moment the Genesis frame is placed outside spacetime, it has no proper time, and multiplying it by 4 × 10¹² is multiplying by nothing.  The argument cannot claim the authority of physics and exemption from it at the same time.  Salviander states the outside-spacetime position explicitly,⁵ which is candid, and it is the point at which the model stops being physics.

"The six-day figure is too good to be a coincidence."  It is not a coincidence and it is not a prediction either.  The starting temperature was chosen, the decay law was chosen, the half period was chosen to equal one Genesis day, and when the published age of the universe fell from 16 billion to 14 billion, the temperature in the denominator was revised upward from the measured 2.73 K to a hypothetical 3.03 K, which lowered the output by exactly the ten percent needed.¹⁰  A number that tracks the literature is being read out of the literature.

"Creationists have already refuted this."  Partly.  The published creationist critique gets the Hebrew right, the arithmetic right, the arbitrariness of the starting ratio right and Genesis 1:16 right.  It also attributes to Schroeder an "edge of the universe" mechanism he explicitly disclaims, and mixes a theological objection in with the physical ones.²  A refutation that misdescribes its target is not usable, and this site will not use it.

"Whatever the physics, the days must be twenty-four hours, so the model is ruled out on exegesis alone."  That is close to Lisle's position and it is a coherent one, but it is not an argument this article rests on.  Schroeder also holds the days to twenty-four hours.  The disagreement is about where the clock sits, and that is settled here on physics:  there is no clock in the universe reading six days, and the frame in which the universe is at rest is measured, is the frame Earth is nearly in, and reads 13.8 billion years.¹⁶

"Then why does the four-day number come out at all?"  Because the comoving horizon in units of an early clock tick is a large but not absurd number, and dividing 46 billion years of conformal time by 4 × 10¹² lands near a few days for the same reason that dividing the age of the universe by the same factor does.  It is arithmetic, not harmony.  The test is what the number then predicts, and what it predicts is six days that get longer, which is the reverse of the text.¹⁵

Sources