SETI and the Testing of Quantum Gravity
Dr. Peter Wilson
Emeritus Professor of Mathematics, University of Sydney
October 14, 1998
The Drake Equation, which provides an estimate of the number, N, of
technological civilizations which might exist in the universe, depends
critically on the probability, fl, that life will
have arisen spontaneously on any planet on which the physical conditions
are favourable during the ~15 billion years
since the Big Bang. Despite the optimism of some of its adherents, SETI
must face the fact that the most favourable estimate of the biochemical
probability of the spontaneous emergence of life (by Bernd-Olaf Küppers1)
is only 10-130, which would yield a negligibly small value
for N. Other estimates of fl are even smaller,
Fred Hoyle2 advocating a value of 10-40,000. If
either of these estimates are of the right order, then the further expenditure
of research funds on SETI would be hard to justify.
However, life has indeed arisen on at least one of the ~1020
planets in the universe, and this implies that the empirical value of
fl must be at least 10-20. Although even
this would yield a value for N of only 10-10, it must
raise doubts whether the biochemical probability is correct or is even
appropriate to this situation.
If an honest coin is tossed 430 times, the probability of getting 430
heads is (½)430 or 10-129.5, which is comparable
to the biochemical probability of life. If this experiment were repeated
1020 times, the chance that any one of these trials of 430
tosses might lead to an all-heads result would still be only one in
10109.5. Thus if this result were actually to occur during
a run of 1020 such trials, we could conclude only that either
a miracle had taken place or that the coin was unfairly loaded.
In the same way if there are of the order of 1020 planets
in the universe, then the probability of life arising naturally on at
least one of these is 10-110. However, we are undoubtedly
here, and it must follow from the coin tossing argument that either
a miracle has occurred (as the creationists would have us believe) or
'the coin was loaded', i.e. the biochemical probability is too low and
some other influence must have intruded on the processes which have
been proposed.
The problem which faced the biochemists was to understand how the first
cell could have been formed without the guidance of some template or
design plan whereby its inanimate components could be brought together
in the correct order to form the first living cell, which could then
give rise to the enzymes necessary to guide the structure of the next
cell, and so on. If no such guidance had been available, i.e. had it
been a random event, then probabilities of the order quoted seemed inevitable.
Here the rather arcane concepts of the theory of quantum gravitation
provide an unexpected clue.
Stephen Hawking3 has proposed that the origin and history
of the universe must be regarded in terms of the theory of quantum gravitation,
and he postulates a universe which is finite in space-time, yet has
no singularities which require the specification of initial conditions
at some space-time boundary. Although we do not yet have a complete
and consistent theory of quantum gravitation, Hawking is confident that
one of the features of such a theory would incorporate Feynman's theory
of the Sum over Histories. In this approach, a particle has not
just one history, as it would in classical theory. Instead, it is supposed
to follow every possible path, or trajectory, in space-time, and with
each of these trajectories there are associated two numbers, the amplitude
and phase of its wave function. The probability that a particle passes
through a particular point in space-time can then be found by summing
the squares of the amplitudes of every possible history that passes
through that point.
It is important to realize that the concept of space-time entails that
'real time' t is replaced by 'imaginary time', it, where
is the imaginary
number and that this four-dimensional space-time is Euclidean, that
is the time dimension, it, is indistinguishable any of the space
dimensions. Hawking argues that, because the imaginary time dimension
is on the same footing as the space dimension, there is the possibility
that space-time can be finite in extent and yet have no singularities
or initial conditions at some boundary or edge, at which the laws of
Physics are inapplicable. Thus there would be no need to specify the
conditions at the boundary: "the boundary condition of the universe
is that it has no boundary," he says.
Since in Euclidean space-time, the imaginary time dimension is indistinguishable
from the spatial dimensions, the concept of a 'history' being of that
which is past has no meaning, trajectories in space-time may go forward
or backward in imaginary time, just as they may move to the left or
the right, or up and down in 3-space. And if the quantum-mechanical
state of a particle at some point in space-time is determined by the
sum of 'histories' of its possible trajectories, the 'historical trajectory'
may equally include contributions from regions with positive values
of it and those with negative values.
This concept may be used in relation to the formation of the first
living cell. Consider the quantum state of a carbon atom which forms
part of a nucleic acid molecule at some point in space-time. Now we
know that it is perfectly possible for that molecule be part of a living
cell or part of an inanimate molecular cloud, because we observe both
states; so the possible trajectories for the wave function for that
carbon atom may include being a component of both inanimate matter and
living matter, and its current quantum state includes information from
the sum of all these trajectories.
So on this hypothesis, the template or design is available in the quantum
states of the atoms which form part of a cell and it would not be surprising
that living cells can be formed from their component parts under the
appropriate conditions. Thus life is part of a living intelligent quantum-mechanical
universe, and the quantum-mechanical value of fl may
be increased from the biochemical value of ~10-130,
or the empirical value of ~10-20
to something of order 10-1.
We must emphasise that this is purely a speculative hypothesis, but
it is not without scientific merit. The philosopher of science, Karl
Popper, has argued that the important criterion for any scientific hypothesis
is that it should lead to observable testing and thus be refutable.
The theory of quantum gravitation as crudely outlined above does lead
to a testable prediction, for if it entails that fl
is of order 10-1, then the Drake number may be as high as
108. Thus many other intelligent populations should exist
within our galaxy and should be detectable by SETI. The SETI program
thus can be regarded as crucial test, in the Popperian sense, of the
theory of quantum gravitation.
SETI programs have indeed been established for some 50 years, yet there
is NO confirmed evidence of the existence of extra-terrestrials, and
such a large value of N raises the inevitable question; where
are they now, why are they not here? Clearly, the result of this test
is, so far, negative.
However, as the Michaelson-Morely experiment demonstrated so convincingly,
even negative results can have important scientific consequences. Fifty
years of testing would seen to be a vanishingly short time on the scales
we are contemplating, and theories, such as that of quantum gravitation
are of no little significance to our understanding of the universe in
which we live. Thus, even if the SETI program fails to discover any
extra-terrestrial civilizations, it may be justified for at least a
similar period by providing a (possibly negative) crucial test of this
theory.
References
- Küppers, B. O., Molecular Theory of Evolution, Springer-Verlag, New
York, 1983.
- Hoyle, F., The Intelligent Universe, Michael Joseph, London,
1983.
- Hawking, S., A Brief History of Time, The University Press,
Cambridge, 1988.
