The Age of the Earth 1

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The Age of the Earth 1

• Kelvins challenge to geology

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Kelvin, Huxley
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Darwin, T.C. Chamberlain
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Lyell and Darwin

• Darwin relied on Lyells position concerning the
  age of the earth.
• He calculated, in the first edition of the
  Origin, how long the denudation (erosion) of a
  region of England called the Weald (which goes
  back to the Carboniferous) had taken.
• The figure he arrived at was (by our standards
  today) pretty good 300 million years.
• But he was soon to regret his boldness in
  actually specifying a number.

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Kelvin

• The most famous physicist of his time.
• Kelvin made important contributions to the
  development of thermodynamics.
• In particular, he identified/contributed to the
  expression of the second law (that entropy always
  increases connected to the fact that heat always
  flows from hotter to cooler).
• But this brings us back to the kind of
  calculation of the earths age that Buffon
  attempted.
• Similarly, it suggests the possibility of
  calculating how long the sun could radiate energy
  at its present rate.

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The Problem

• Kelvin arrived at a simple model of the earth
• It had solidified pretty well all at once (until
  that point, it would be kept uniformly hot
  mixed by convection currents).
• From that point it would behave like any hot
  sphere, beginning at the melting temperature and
  gradually radiating heat outwards to space
  (temperature there is just above absolute zero).
  
• There is plenty of evidence that temperature
  increases as we dig or drill deeper into the
  earth this was well-known.
• The calculations for temperature profiles over
  time of a solid, uniform sphere depend only on
  the initial temperature, the heat capacity and
  conductivity of the material.
• The upshot is that there are limits to how old
  the earth is on this model, and when he applied
  it, Kelvin arrived first at an upper limit of 400
  million years and a lower limit of 40 million
  years he preferred about 100 million as the best
  estimate

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The Sun

• Helmholtz had proposed a gravitational theory of
  the suns energy.
• Beginning with small bodies spread out through
  space, which then come together under the
  influence of gravity, we can calculate the amount
  of energy available to power the sun.
• This gravitational theory allows far more energy
  in total than any form of combustion could (the
  sun would go out within some thousands of years
  if it were a burning lump of coal).
• Kelvin adopted this theory concluded that the
  sun could provide something like the present
  level of energy for something like 100 million
  years, with 500 million as an outside limit.
• Again, the main point for Kelvin was that the
  time was limitedhe rejected Lyells appeal to
  drafts on the bank of time as irresponsible.
• Darwin was roundly criticized for his own
  calculation, which non-uniformitarians and fans
  of Kelvin dismissed as absurd.

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Comparing ways of measuring time

• Geologists had various processes erosion,
  sedimentation,
• Each process produces a kind of cumulative
  measure, just like an hour-glass.
• If we can combine a rate with a measure of how
  much of the process has taken place, we will get
  a time.
• This kind of measure is pretty elasticits hard
  to say just how fast or slow erosion or
  sedimentation is over the long run (even if we
  measure the sediment carried by a river over a
  year, we still need to know how much area that
  sediment is spread over to build sedimentary
  rock).
• Its also hard to measure just how much erosion
  or sedimentation has occurred (even if we add up
  the thicknesses of sedimentary rocks to form a
  column, its hard to be sure weve got it all,
  with no overlaps).

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The Geological Estimates

• Many of these estimates were made following
  Kelvins initial work.
• They tended to come out roughly in agreement with
  Kelvins 100 million years.
• But they are clearly pretty elastic.
• On the other hand, if we can specify maximum
  rates and minimum accumulations with good
  confidence, we can put a lower limit on the time
  required.

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The Physical Estimates

• Kelvins methods depended on Kelvins models.
• Kelvins model of the earth treated it as solid.
  There was real evidence for this, but the
  evidence was not conclusive.
• John Perry added convection below the surface to
  Kelvins model of the earth the result was a
  huge increase in the time available.
• Also, of course, any source of heat that could
  replace the heat lost to space would put the
  calculations out of whack.
• But Kelvin was right in terms of the physics
  known at the time There was no credible source
  of energy that could do it.

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The Sun

• The models of the sun were much simpler they
  didnt depend on solidity. They only depended on
  the gravitational theory of the suns energy. It
  would be quite difficult to find, in 19th century
  physics, a way of packing more energy in.
• So the limit of 100 million years for the sun,
  which was later reduced to something like 25
  million (1899). Later calculations based on new
  figures, some from King and with support from
  another hard-liner, Tait, reduced Kelvins
  estimate of the age of the earth to 40 million or
  less.

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Reaction

• Huxley had resisted Kelvins calculations from
  the outset, pointing out that they depended on
  substantial and unproven assumptions, and that
  even if there were limits to time, nothing in the
  geologists evidence suggested those limits had
  made a difference to the history we now see in
  geological record .
• These new limits, which were laid down in the
  1890s, sparked a resistance amongst geologists.
• James Croll and T.C. Chamberlain were supporters
  of this kind of calculation, but they were also
  convinced that the geological evidence showed the
  earth could not be that young.
• So were at an impasse.

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Pecking order

• When two sciences seem to disagree about a
  question that both have something to say about,
  what do we do? Who should we believe?
• Kelvins view was that geology should take its
  time from physics and make whatever adjustments
  it had to.
• Chamberlain and Croll held that geology should
  deal with its own evidence, develop and work on
  it independently, and hold its ground.
• Perry offered a compromise, but it couldnt help
  with the suns energy.

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Upshot

• Radioactivity Rutherford
• Behold, the old boy beamed.
• The energy released in radioactive decay is much
  much higher than that produced by the burning of
  a similar mass of material.
• This can replace heat lost by the earth and (much
  more important) provide a source of energy that
  could power the sun for much longer than Kelvin
  had allowed.

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Better yet

• As radioactivity came to be better understood
  (including isotopes their relations, nuclear
  physics in general, half-lives etc.) it became
  evident that we could use these elements as
  geological clocks.
• Holmes and others developed the techniques.
• The upshot is the present measures of geological
  ages and the overall age of the earth, which have
  been very stable since the middle of the 20th
  Century.