In
the new book The Improbability Principle, mathematician David
J. Hand looks at the issue of apparent cosmic fine-tuning, the many
ways in which the universe seems to be tailor-made for the existence
of intelligent beings such as us. Hand attempts to explain this
away in keeping with his overall thesis that we should not be
surprised when incredibly improbable things happen.
Hand
looks at the fact that the existence of stars requires an exquisite
balance between two of the fundamental forces of the universe, the
gravitational force and the electromagnetic force. He suggests that
thinking there is such a balance results from the mistake of
considering that just one of the two has been fine-tuned to just the
right value. When we consider the possibility of both varying, Hand
suggests, then the situation is not so amazing. As Hand says on page
214-215 of his book:
We
saw that changing the value of either one of these values would mean
that the universe would not be suitable for life. But what if we
changed them both? What if we increased the electromagnetic force a
little, to match the increase in the gravitational force? Do this
approximately, and the equilibrium within stars is maintained, so
perhaps planets still form and life evolve. Fine-tuning, yes, but
with much, much more scope for a pair of values which will lead to
life than if the forces must separately take highly specific values.
Hand's
reasoning is incorrect. When we have a case in which two fundamental
constants of nature are exquisitely balanced, there is no greater
likelihood that both will balance if we allow for the possibility of
both of them varying. We can see this clearly by considering the case
of the proton charge and the electron charge.
There
is an exquisite and unexplained balance between the proton charge and
the electron charge, in that all protons have a charge of exactly
1.602176565 X 10-19 coulomb, and all electrons have a
charge of exactly -1.602176565 X 10-19 coulomb (which is
quite amazing given that each proton has a mass 1836 times greater
than the mass of each electron). As the astronomer Greenstein has
pointed out, there are reasons why stars and planets would not be
able to exist if the absolute value of the proton charge and the
electron charge differed by even 1 part in 1,000,000,000,000,000,000.
Since electromagnetism is a force more than a trillion trillion
trillion times greater than the gravitational force, even a tiny
change in either the proton charge or the electron charge would mean
that electromagnetic effects acting on a large body would overwhelm
gravitational effects, and gravitation would be insufficient to keep
stars and planets together.
But
suppose we imagine random changes in both the electron charge and the
proton charge. Would that increase the probability of the two of them
matching in the way that is necessary for stars and planets to hold
together? No, it wouldn't. If we imagine both constants randomly
changing, it is true that this would open up many new possibilities
that might be compatible with the existence of stars and planets,
such as one in which the proton charge was 3.378921 X 10-12
coulomb and the electron charge was an exactly opposite value
of -3.378921 X 10-12 coulomb. But the overall likelihood
of an exact match when both constants vary is not any greater than if
one allows only one constant to vary.
Similarly,
imagine I am playing a casino "million dollar jackpot" game of chance, and start with one
random number between 1 and a million. To win, I have to get from the
casino another number that matches the first number. If only the
second number varies, the chance of success is 1 in a million. Now
the casino employee may tell me: increase your chances by letting
both numbers be random. But that's a fallacy – my chances of
success will not be increased. The probability of getting a match if
you start with one number and then get a random number is 1 in a
million. The probability of getting a match if you get two random
numbers is one million out of a trillion (because there are one million
possible matches of two numbers between 1 and a million, and a
trillion different possible combinations of two numbers between 1 and a
million). But one million out of a trillion is a probability exactly
the same as 1 in a million.
Hand
then asks us to consider another possibility – that there may be
some hidden reason why a change in one fundamental constant might
cause a corresponding change in another very different fundamental
constant. This might help to explain the exquisite balances within
nature, Hand suggests. But this suggestion is an appeal to an
imaginary possibility, and Hand provides no facts to back up such a
suggestion. To the best of our knowledge, fundamental constants on
which life depends (such as the speed of light, the gravitational
constant, Planck's constant, the proton charge, and the electron
charge) are entirely independent. There's no reason to think that
having one such constant be compatible with life would increase the
chance that other such constants would be compatible with life.
Hand
tries to pass off his groundless imaginary idea as an example of what
he calls the “law of the probability lever.” Similarly, if a
husband had failed to save enough money for retirement, and his wife
complained, the husband could imagine that fairies will give him a
million dollars when he reaches the age of 62, and he might call such
a fantasy “the law of the fairy contributions.” Imaginary
concepts for which there is no factual basis should not be referred
to as laws.
Hand
then refers to a scientific paper in which one physicist claimed to
show that it's not all that unlikely that stars should exist in
random universes. Hand summarizes the paper by Adams as follows:
Fred
C. Adams, of the Michigan Center for Theoretical Physics,
investigated varying the gravitational constant, the fine-structure
constant, and a constant determining nuclear reaction rates. He found
that about a quarter of all possible triples of these three values
led to stars which would maintain nuclear fusion – like the stars
in our universe. As he said, “[We] conclude that universes with
stars are not especially rare (contrary to previous claims).”
The
previous claims Adams referred to are numerous claims made in the
scientific literature along the lines that the chance is incredibly
low of a random universe allowing stars like ours. There are some
reasons why such claims were actually correct, and why Adams is wrong
on this issue.
The
first reason is that to have any stars at all you need to have a
fine-tuning of not just the three constants Adams considered, but
other constants he did not consider. For example, Adams completely
fails to consider the very precise match between the proton charge
and the electron charge needed for the stability of large bodies like
planets and stars (previously discussed), a match that would not occur by chance in 1 in
1,000,000,000,000 universes in the parameter space he considers.
The
second reason is that the real question is not the likelihood of some
type of stars, but yellow stars like the sun, which offer better
prospects for the evolution of intelligent life than other types of
stars such as red dwarfs or blue giants. Scientists such as Paul
Davies have concluded that very small changes in the fundamental
constants would preclude the existence of stars like the sun. It's
kind of like this: nature must thread one needle hole for there to
exist some type of stars, but nature must thread a much tinier needle
hole for there to be stars like the sun.
The
third reason is that Adams is guilty of a fallacy that we might call
the fallacy of the “ant near the needle hole.” Consider an ant
that somehow wanders into your sewing kit. If it were smart enough to
talk, the ant might look at the eye of a needle hole in your sewing
kit, and say, “Wow, that's a big needle hole!” Such an
observation will only be made if you have a perspective looking a few
millimeters away from the needle hole.
Similarly,
Adams has given us graphs in which his “camera” is placed a few
millimeters from the needle hole that must be threaded for stars to
exist. He has imagined a parameter space in which fundamental
constants are merely tripled. But physicists routinely deal with a
difference of 40 orders of magnitude
(10,000,000,000,000,000,000,000,000,000,000,000,000,000), which, for
example, is roughly the difference between the strength of the
strong nuclear force and the gravitational force. So if we are
imagining a parameter space of alternate universes, we must imagine a
parameter space infinitely larger than the relatively microscopic
parameter space Adams considered. Rather than just imagining a
possible tripling of the fundamental constants Adams considers, we
should imagine that any of them could vary by a trillion times or a
quadrillion times or a quintillion times.
Taking
that correct perspective, we can see how marvelous it was that nature
managed to thread the needle holes necessary for our existence. You
can visualize it this way. The parameter space is the vast Sahara
desert. The needle holes that nature needed to thread for a
habitable universe are in different random positions scattered
throughout that vast desert. The likelihood of those needle holes being threaded successfully by
chance is therefore infinitely smaller than the probability figure reached by
Adams.
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