The anthropic principle: science, philosophy or guesswork?

THE ANTHROPIC PRINCIPLE:
SCIENCE, PHILOSOPHY OR
GUESSWORK ?
Mariano Artigas
Department of Philosophy
University of Navarra
Pamplona (Spain)
The Impact of the Humanities
on the Development of European Science
SUMMER SCHOOL 10-15 JUNE 2004
Venice (Italy)

Ernan
McMullin
(1981)
Basic science, at its most
innovative, merges into philosophy

Robert Dicke
(1961)
It is well known that carbon is
required to make physicists

Nick Bostrom
(2002)
A total of over thirty
anthropic principles have been
formulated and many of them
have been defined several
times over – in nonequivalent
ways – by different authors,
and sometimes even by the
same authors on different
occasions. Not surprisingly,
the result has been some
pretty wild confusion
concerning what the whole
thing is about.

Contents
1. CONSTANTS OF NATURE AND NATURAL UNITS
2. THE DIMENSIONLESS CONSTANTS OF NATURE
3. DIMENSIONLESS CONSTANTS AND LARGE
NUMBERS
4. THE FORMULATION OF THE ANTHROPIC
PRINCIPLE
5. THE ANTHROPIC PRINCIPLE COMES OF AGE
6. FINE-TUNING, TELEOLOGY, AND OTHER
WORLDS
7. SCIENCE, PHILOSOPHY, OR GUESWORK?

1
CONSTANTS OF NATURE AND
NATURAL UNITS
1.1. The Constants of Nature
1.2. Natural Units: George Stoney
(1874)
1.3. Natural Units: Max Planck
(1899)

1.1. The Constants of Nature
Charge of an electron (e) = 1.602 x 10-19
coulombs
Speed of light in a vacuum (c)= 2.99792458 x 108
m s-1
(roughly 300,000 kilometers per second)
Planck constant (h) = 6.626 176 x 10-34
Js
ħ = h / 2π = 1.054589 x 10-34
Js
Gravitational constant (G) = 6.67259 x 10-11
N m2
kg-2
(m3
kg-1
s-2
)
Fine structure constant (α) α = e2
/ 2ε0 hc ≅ 1 /137
Other universal constants are known (some 19 in total): the
Boltzmann constant, the mass of an electron, the mass of a proton,
Avogadro’s number, the gas constant, the Rydberg constant, and
so on.

John Barrow on the constants of nature
This is the Holy Grail of
fundamental physics and it
means the numerical calculation
of one of the constants of Nature.
This has never been done. So far,
the only way we can know their
values is by measuring them.
This seems unsatisfactory. It
allows the constants that appear
in our theories to have a huge
range of different possible values
without overthrowing the theory
(2002)

1.2. Natural Units:
George Stoney (1874)
(1)
George Johnstone
Stoney
1826-1911

1.2. Natural Units: George Stoney (1874) (2)
M = (e2
/ G)1/2
= 10-7
gram
L = (Ge2
/ c4
)1/2
= 10-37
metres
T = (Ge2
/ c6
)1/2
= 3 x10-46
seconds
45 minutes = 9 x10-44
Stoney-time!

1.3. Natural Units: Max Planck (1899-1900) (1)
m = (hc / G)1/2
= 5,56 x 10-5
gram
l = (Gh / c3
)1/2
= 4,13 x 10-33
cm
t = (Gh / c5
)1/2
= 1,38 x10-43
sec
T = k-1
(hc5
/ G)1/2
= 3,5 x1032
K

1.3. Natural Units: Max Planck (1899-1900) (2)
Planck’s units mark the
boundary of applicability
of our current theories.
The constants of Nature
mark out the frontiers of
our existing knowledge
and show us where our
theories start to overreach
themselves (John Barrow)

2
THE DIMENSIONLESS
CONSTANTS OF NATURE
2.1. Einstein’s Search for the
Ultimate Theory of Physics
2.2. Dimensionless Constants
and Other Worlds

2.1. Einstein’s Search for the
Ultimate Theory of Physics (1)
God does
not play
dice

Albert Einstein (1945) (2)
There are two kinds of
constants: apparent and real
ones. The apparent ones are
simply the outcome of the
introduction of arbitrary units,
but are eliminable. The real
[true] ones are genuine
numbers which God had to
choose arbitrarily, as it were,
when He deigned to create
this world.

Albert Einstein (1945) (3)
Or one could put it like this: In a reasonable
theory there are no dimensionless numbers whose
values are only empirically determinable.
Of course, I cannot prove this. But I cannot
imagine a unified and reasonable theory which
explicitly contains a number which the whim of the
Creator might just as well have chosen differently,
whereby a qualitatively different lawfulness of the
world would have resulted.
Or one could put it like this: A theory which in
its fundamental equations explicitly contains a non-
basic constant would have to be somehow constructed
from bits and pieces which are logically independent
of each other; but I am confident that this world is not
such that so ugly a construction is needed for its
theoretical comprehension.

2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (1)
The identification of dimensionless constants of
Nature like α and αG , along with the numbers that
play the same defining role for the weak and strong
forces of Nature encourages us to think for a
moment about worlds others than our own. These
other worlds may be defined by laws of Nature
which are the same as those which govern the
Universe as we know it but they will be
characterised by different values of dimensionless
constants. These numerical shifts will alter the
whole fabric of our imaginary worlds. The
balances between their forces will be different
from those in our world. Atoms may have different
properties. Gravity may play a role in the small-
scale world. The quantum nature of reality may
enter in unexpected places.
α = 2π e2
/ hc
≈ 1 / 137
αG= Gmpr
2
/hc
≈ 10-38

2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (2)
The last important lesson we learn from the way that pure
numbers like α define the world is what it really means for
world to be different. The pure number that we call the
fine structure constant and denote by α is a combination of
the electron charge, e, the speed of light, c, and Planck’s
constant, h. At first we might be tempted to think that a
world in which the speed of light was slower would be a
different world. But this would be a mistake. If c, h and e
were changed so that the values they have in metric (or
any other) units were different when we looked them up in
our tables of physical constants, but the value of α
remained the same, this new world could be
observationally indistinguishable from our world. The
only thing that counts in the definition of the world are the
vales of the dimensionless constants of Nature. If all
masses are doubled in value you cannot tell because all
the pure numbers defined by the ratios of any pair of
masses are unchanged

3
DIMENSIONLESS CONSTANTS AND
LARGE NUMBERS
3.1. Constants of Nature and Large
Numbers:
Sir Arthur Eddington (1935)
3.2. Large Number’s Coincidences
Are Not Accidental:
Paul Dirac (1937)

3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (1)
Four pure dimensionless numbers
(the ultimate constants)
Ratio of the masses of the proton
and electron: mpr / me ≈ 1840
The inverse of the fine structure
constant: 2πh / e2
≈ 137
Ratio of the gravitational force to
the electromagnetic force between
and electron and a proton:
e2
/ Gmprme ≈ 1040
Number of protons in the visible
universe: NEdd ≈ 1080
(1882-1944)

3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (2)
Are these four constants irreducible, or
will a further unification of physics
show that some or all of them can be
dispensed with? Could they have been
different from what they actually are?...
the question arises whether the above
ratios can be assigned arbitrarily or
whether they are inevitable. In the
former case we can only learn their
values by measurement; in the latter
case it is possible to find them by
theory... I think the opinion now widely
prevails that the [above four]
constants... are not arbitrary but will
ultimately be found to have a theoretical
explanation; though I have also hears
the contrary view expressed.

Dimensionless numbers with an “strange”
appearance: related with 1040
, its squares and cubes
Total number of protons in the observable
universe: 1080
Ratio of the strengths of electromagnetic and
gravitational forces between two protons: 1040
“Action” of the observable universe in units of the
fundamental Planck units of action: 10120
Cosmological constant in units of the square of the
Planck length: 10-120

John D. Barrow on Eddington
Eddington had tried to build a theory that made their
[large numbers] appearance understandable. But he
failed to convince a significant body of cosmologists
that he was on the right track. Yet Eddington
succeeded in persuading people that there was
something that needed explaining. Completely
unexpectedly, it was one of his famous neighbours in
Cambridge who wrote the short letter to the journal
Nature which succeeded in fanning interest in the
problem with an idea that remains a viable possibility
even to this day [Paul Dirac].

3.2. Large Number’s Coincidences Are Not Accidental: Paul Dirac (1937)(1)
(1902-1984)
Now, you might say, this is a remarkable
coincidence. But it is rather hard to believe
that. One feels that there must be some
connection between these very large numbers,
a connection which we cannot explain at
present but which we shall be able to explain
in the future when we have a better
knowledge both of atomic theory and of
cosmology.
Let us assume that these two numbers are
connected. Now one of these numbers is not a
constant. The age of the universe, of course,
gets bigger and bigger as the universe gets
older. So the other one must be increasing
also in the same proportion.
Large Numbers Hypothesis

Paul Dirac (2)
Any two of the very
large dimensionless
numbers occurring in
Nature are connected
by a simple
mathematical relation,
in which the
coefficients are of the
order of magnitude
unity.

4
THE FORMULATION OF THE
ANTHROPIC PRINCIPLE
4.1. Introducing Anthropic Reasoning:
Gerald Whitrow (1955)
4.2. More Anthropic Reasoning:
Robert Dicke (1961)
4.3. The principle is Almost There:
Collins and Hawking (1973)
4.4. The Birth of the Anthropic Principle:
Brandon Carter (1973)

4.1. Introducing Anthropic Reasoning:
Gerald Whitrow (1955)
I suggest that a possible clue to the
elucidation of this problem is provided by
the fact that physical conditions on the
Earth have been such that the evolution of
Man has been possible.
A new attempt to throw light on the
question indicates that this fundamental
topological property of the world may
possibly be regarded as partly contingent
and partly necessary, since it could be
inferred as the unique natural concomitant
of certain other contingent characteristics
associated with the evolution of the higher
forms of terrestrial life, in particular of
Man, the formulator of the problem.
1902-2000

4.2. More Anthropic Reasoning: Robert Dicke (1961)
with the assumption of an
evolutionary universe, T [the Hubble
age of the universe] is not permitted
to take one of an enormous range of
values, but is somewhat limited by
the biological requirements to be met
during the epoch of man.
Thus, contrary to our original
supposition, T is not a “random
choice” from a wide range of
possible choices, but is limited by the
criteria for the existence of
physicists.

4.3. The principle is Almost There:
Collins and Hawking (1973)

Brandon Carter (1973) (1)
ANTHROPIC PRINCIPLE
what we can expect to
observe must be restricted
by the conditions necessary
for our presence as
observers. (Although our
situation is not necessarily
central, it is inevitably
privileged to some extent).

WEAK ANTHROPIC
PRINCIPLE
We must be prepared to take
account of the fact that our
location in the universe is
necessarily privileged to the
extent of being compatible
with our existence as
observers

STRONG ANTHROPIC
PRINCIPLE
The Universe (and hence the
fundamental parameters on
which it depends) must be
such as to admit the creation
of observers within it at
some stage. To paraphrase
Descartes, “Cogito ergo
mundus talis est”

Carter on Anthropic Principle, 1973 (1)
It is of course always philosophically possible – as
a last resort, when no stronger physical argument is
available - to promote a prediction based on the
strong anthropic principle to the status of an
explanation by thinking in terms of a “world
ensemble”... The existence of any organism
describable as an observer will only be possible for
certain restricted combinations of the parameters,
which distinguish within the world-ensemble an
exceptional cognizable subset.

Carter on Anthropic Principle, 1973 (2)
The acceptability of predictions of this kind
as explanations depends on one’s attitude to
the world ensemble concept. Although the
idea that there may exist many universes, of
which only one can be known to us, may at
first sight seem philosophically undesirable, it
does not really go very much further than the
Everett doctrine to which one is virtually
forced by the internal logic of quantum
theory.

5
THE ANTHROPIC PRINCIPLE
COMES OF AGE
5.1. Life Depends on Delicate
Coincidences: Carr & Rees (1979)
5.2. A Meeting of the Royal Society
(1983)
5.3. Carter Revisited by Carter (1983)
5.4. John D. Barrow and Frank J. Tipler
on the Anthropic Principle (1986)

5.1. Life Depends on Delicate Coincidences:
Carr & Rees (1979) (1)
Sir Martin Rees
Several aspects of our
Universe – some of which
seem to be prerequisites
for the evolution of any
form of life – depend
rather delicately on
apparent ‘coincidences’
among the physical
constants

Carr & Rees (1979) (2)
Sir Martin Rees
The possibility of life as
we know it evolving in the
Universe depends on the
values of a few basic
physical constants – and is
in some respects
remarkably sensitive to
their numerical values

Carr & Rees (1979) (3)
Sir Martin Rees One day, we may have a more
physical explanation for some of
the relationships discussed here
that now seem genuine
coincidences... However, even if
all apparently anthropic
coincidences could be explained
in this way, it would still be
remarkable that the relationships
dictated by physical theory
happened also to be those
propitious for life.

5.2. A Meeting of the Royal Society (1983)
interest in [anthropic principle] in recent times
originally instigated the proposal to hold this
Discussion. However, because of their
speculative character and of their inability as
yet to produce new predictions, it was
considered that the main emphasis ought to be
upon the study of the constants themselves
rather than the role of the constants in these
applications.

5.3. Carter Revisited by Carter (1983) (1)
The practical scientific utility of this principle
arises from its almost tautological corollary to the
effect that in making general inferences from what
we observe in the Universe, we must allow for the
fact that our observations are inevitably biased by
selection effects arising from the restriction that
our situation should satisfy the conditions that are
necessary a priori, for our existence. The term self-
selection principle would be an alternative and
perhaps more appropriate description for this
hardly questionable but easily overlooked precept.

If I had guessed that the term ‘anthropic principle’
would come to be so widely adopted I would have
been more careful in my original choice of words.
The imperfection of this now standard terminology
is that it conveys the suggestion that the principle
applies only to mankind. However, although this is
indeed the case as far as we can apply it ourselves,
it remains true that the same self-selection
principle would be applicable by any
extraterrestrial civilization that may exist.

As I originally formulated it (Carter 1974) this
‘strong’ principle consisted in the remark that our
mere existence as intelligent observers imposes
restrictions not just on our situation but even on
the general properties of the Universe, including
the values of the fundamental parameters that are
the subject of the present meeting. Although this
‘principle’ has aroused considerable enthusiasm in
certain quarters, it is not something that I would be
prepared to defend with the same degree of
conviction as is deserved by its ‘weak’ analogue.

5.4. Barrow and Tipler on the Anthropic Principle (1986) (1)
WEAK ANTHROPIC PRINCIPLE
The observed values of all physical and
cosmological quantities are not equally probable
but they take on values restricted by the
requirement that there exist sites where carbon-
based life can evolve and by the requirement that
the Universe be old enough for it to have already
done so.
Much stronger than Carter’s weak principle

5.4. Barrow and Tipler on the Anthropic Principle (1986) (2)
STRONG ANTHROPIC PRINCIPLE
The Universe must have those properties
which allow life to develop within it at
some stage in its history.
If we speak of this universe where we are, yes, of course
If we speak of universes in general, why?

Confusion increases: an example
Later, Carter also proposed the Strong
Anthropic Principle (SAP), which states that
the Universe had to bring humanity into
being. This version is much more
teleological, if not theological, and is of a
highly speculative nature. Nonetheless,
Carter had scientific reasons to propose it.

6
FINE-TUNING, TELEOLOGY,
AND OTHER WORLDS
6.1. Fine-Tuning
6.2. The Teleological Argument
6.3. Many Worlds
6.4. Observation Selection Effects

6.1. Fine-Tuning
One aspect of anthropic reasoning that has attracted plenty of
attention, from both philosophers and physicists, is its use in
cosmology to explain the apparent fine-tuning of our universe.
“Fine-tuning” refers to the supposed fact that there is a set of
cosmological parameters or fundamental physical constants
that are such that had they been very slightly different, the
universe would have been void of intelligent life. (Nick
Bostrom)
EXAMPLES
- rate of expansion of the universe
- relations between fundamental masses and forces
- topological and metrical properties of space-time

6.2. The Teleological Argument (1)
The fifth way is taken from things’ being
directed. We see that there are things that
have no knowledge, like physical bodies, but
which act for the sake of an end. This is clear
in that they always, or for the most part, act in
the same way, and achieve what is best. This
shows that they reach their end not by chance
but in virtue of some tendency. But things
which have no knowledge do not have a
tendency to an end unless they are directed by
something that does have knowledge and
understanding. An example is an arrow
directed by an archer. Therefore there is some
being with understanding which directs all
things to their end, and this, we say, is God.
Thomas Aquinas

It is impossible for things contrary
and discordant to fall into one
harmonious order always or for the
most part, except under some one
guidance, assigning to each and all a
tendency to a fixed end. But in the
world we see things of different
natures falling into harmonious order,
not rarely and fortuitously, but always
or for the most part. Therefore there
must be some Power by whose
providence the world is governed;
and that we call God
6.2. The Teleological Argument (2)
Thomas Aquinas

6.3. Many Worlds (1)
Some philosophers and physicists take
fine-tuning to be an explanandum that
cries out for an explanans. Two
possible explanations are usually
envisioned: the design hypothesis and
the ensemble hypothesis. Although
these explanations are compatible,
they tend to be viewed as competing.
If we knew that one of them were
correct, there would be less reason to
accept the other.
Nick Bostrom

In contrast to some versions of the
design hypothesis, the meaningfulness
of the ensemble hypothesis is not
much in question. Only those
subscribing to a very strict
verificationist theory of meaning
would deny that it is possible that the
world might contain a large set of
causally fairly disconnected spacetime
regions with varying physical
parameters.
Nick Bostrom

Cosmologists have suggested
numerous ways in which greatly
many, greatly varied universes
could be generated... In short,
modern theorists find it easy to
invent mechanisms for making
apparent physics and overt
properties differ from one universe
to another even when the
underlying physics and the most
fundamental properties remain
always the same.
John Leslie

In my model, I assume that our Universe did indeed
appear from nowhere about 1010
yr ago. Contrary to
widespread belief, such an event need not have
violated any of the conventional laws of physics.
The laws of physics merely imply that a Universe
which appears from nowhere must have certain
specific properties. In particular, such a Universe
must have a zero net value for all conserved
quantities... I offer the modest proposal that our
universe is simply one of those things which
happen from time to time.
E. P. Tryon, “: Nature, 246 (1973), No. 5433, pp. 396-397

6.3. Many Worlds (5) Max Tegmark

Max Tegmark
(Scientific American, May 2003)
Not just a staple of science fiction, other universes are a direct
implication of cosmological observations.
Is there a copy of you reading this article? A person who is not
you but who lives on a planet called Earth, with misty mountains,
fertile fields and sprawling cities, in a solar system with eight other
planets? The life of this person has been identical to yours in every
respect. But perhaps he or she now decides to put down this article
without finishing it, while you read on...
... In infinite space, even the most unlikely events must take place
somewhere. There are infinitely many other inhabited planets,
including not just one but infinitely many that have people with the
same appearance, name and memories as you, who play out every
possible permutation of your life choices.

Max Tegmark
(Scientific American, May 2003)
The Reality Postulate
One of the many implications of recent
cosmological observations is that the
concept of parallel universes is no mere
metaphor. Spare appears to be infinite in
size. If so, then somewhere out there,
everything that is possible becomes real, no
matter how improbable it is...
... And this is fairly solid physics.

Alan Guth
the
inflationary
universe

The inflationary universe
One of the intriguing consequences of inflation is that
quantum fluctuations in the early universe can be stretched to
astronomical proportions, providing the seeds for the large
scale structure of the universe. The predicted spectrum of these
fluctuations was calculated by Guth and others in 1982. These
fluctuations can be seen today as ripples in the cosmic
background radiation, but the amplitude of these faint ripples
is only about one part in 100,000. Nonetheless, these ripples
were detected by the COBE satellite in 1992, and they have
now been measured to much higher precision by the WMAP
satellite and other experiments. The properties of the radiation
are found to be in excellent agreement with the predictions of
the simplest models of inflation.

Andrei
Linde
eternal
chaotic
inflation?

Eternal chaotic inflation
Initially, inflation was considered as an intermediate stage
of the evolution of the universe, which was necessary to
solve many cosmological problems... inflation was a part
of the big bang theory. Gradually, however, the big bang
theory became a part of inflationary cosmology. Recent
versions of inflationary theory assert that instead of being
a single, expanding ball of fire described by the big bang
theory, the universe looks like a huge growing fractal. It
consists of many inflating balls that produce new balls,
which in turn produce more new balls, ad infinitum.
Therefore the evolution of the universe has no end and
may have no beginning.

6.4. Observation Selection Effects
Another example, taken from Sir Arthur
Eddington: suppose you are trying to
catch fish with a net that doesn’t catch
fish that are shorter than 20 cm. If you
use such a net to catch a hundred fish
and they all turn out to be 20 cm or
longer, then obviously you are not
allowed to regard this as evidence that
the minimum length of fish in the lake is
20 cm.
Nick Bostrom
Anthropical reasoning is a kind
of observation selection effect

7
SCIENCE, PHILOSOPHY,
OR GUESWORK?

In the end...
perhaps the most significant change in cosmological thinking
involves a new willingness to discuss what used to be an idea
that was not normally mentioned in polite company: the
anthropic principle... The realization that an extremely small,
but non-zero, cosmological constant might exist has changed
physicists’ interest in anthropic explanation of nature
precisely because the value it seems to take is otherwise so
inexplicable... In the end as with so many anthropic
arguments, it is hard to know what to make of this result,
especially in the absence of any fundamental theory.
Lawrence M. Krauss, “A just-so story”, Nature, vol. 423 (15
May 2003), pp. 230-231.

The anthropic principle: science, philosophy or guesswork?

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The anthropic principle: science, philosophy or guesswork?