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The Inevitability of Fine Tuning in a Complex Universe

May 2011
International Journal of Theoretical Physics 50(5):1577-1601

Authors:

Électricité de France (EDF)

Why should the universe need to be fine tuned? The thesis is presented that parameter sensitivity arises as a natural consequence of the mathematics of dynamical systems with complex outcomes. Hence, fine tuning is a mathematical correlate of complexity and should not elicit surprise. KeywordsFine tuning–Universal constants–Entropy–Complexity–Multiverse

Illustrating a logical fallacy: the observation of fine-tuning in parameters c 1 and c 2 does not imply that they are confined to the red dashed box.

…

Relative abundance of nuclei for =10 6 : Comparison of different B

…

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The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

International Journal of Theoretical Physics

(2011)

, 1577

-1601

The Inevitability of Fine Tuning

in a Complex Universe

R.A.W.

Bradford

Bennerley,

1 Merlin Haven

Wotton

under

Edge

Glos. GL12 7BA

, UK

Tel. 0145

3 843462 / 01452 653237 / 07

805 077729

RickatMerlinHaven@hotmail.com

ABSTRACT

Why should the universe

need to be fine

tuned? The thesis is presented that

parameter sensitivity

arises as a natural consequence of the mathematics of dynamical sy

stems

with complex outcomes

Hence, fine tuning is a mathematical correlate of complexity and should not elicit surprise.

Keywords

Fine tuning, universal constants, entropy, complexity, multiverse

Fine Tuning and the Purpose of this Paper

It is ove

40 years since Carter

[15

]

observed that the universal constants

of physics

appear to be peculiarly fine tuned. Relatively small variations in the

universal

constants

it is claimed,

would

produce radical changes in the universe.

On first acquaintance th

seems remarkable and surprising. It will be argued here that, on the contrary, the fact that

the universe contains complex parts makes fine tuning inevitable. Had physicists

been

foresighted enough, fine tuning could have been anticipated even before ph

ysics

and

cosmology

had advanced to the stage where it could be directly demonstrated.

To make clear what

mean by fine tuning

a few examples

are given

in section 2.

shall argue that, whil

st the tuning of some universal constants may

not

as num

erically

impressive as is sometimes claimed, nevertheless tuning is evident.

What has not been

brought out clearly before is that fine tuning consists of two separate phenomena

parameter sensitivity and fine tuning itself

This is explained in section 3

In section 4

some toy models are used to explain why parameter sensitivity is to be expected in any

universe with a complex outcome. Section 5 then presents our general thesis that

parameter sensitivity is a mathematical result of the e

volution

of complexi

ty, the tw

issues

being linked via

entropy interpreted in terms of phase space volume. Section 6

discusses

briefly the relevance of this work to the cosmological constant, the causal

entropic principle, the creationist argument from design and multiverses

2 Examples of Fine Tuning

2.1

Varying Single Parameters

Illustrates Tuning

A few examples of fine tuning are given below.

However, there are many further

examples and these matters have been discussed many times before, see for example

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

,3,6,7,13-1

6,20

-24

The commentary on each example explains why

some of them

may not be as impressive as they first appear.

(i)

f the neutron were lighter by more than 0.08%, or if it were heavier by more than

~1%, then there would be no stable atomic matte

r in the universe.

This narrow mass

range is required to avoid both nuclear capture of the atomic electrons, and also beta

decay of the nucleus.

(ii)

If the weak

nuclear force were

sufficiently

weaker then the abundance of neutrons

and protons after the first f

ew seconds would have been closely matched

and

Big

Bang N

ucleosynthesis (BBN)

would have resulted

in a universe consisting of

virtually all helium and very little hydrogen. A universe with no hydrogen would

contain no water, no hydrocarbons such as amino a

cids, and

no hydrogen bond

chemistry, and hence no

life as we know it

However we shall see below that

sufficiently weaker really means a lot weaker, by at least an order of magnitude.

(iii)

If the strong nuclear force (i.e., the effective low energy coupling

, g

) were ~15%

weaker then the deuteron would be unbound

. T

he formation of

all nuclei would be

prevented and there would be no chemical elements other than hydrogen.

(iv)

If the strength of the strong nuclear force, g

, were changed by

the rate of the

triple

alpha reaction would be affected so markedly that

the production of biophilic1

abundances of either carbon or oxygen would be prevented.

Example (i)

seems impressive, but becomes much less so when it is recalled that the

neutron and

the proton share a common structure. About 99% of a nucleon s mass is due

to the virtual gluons and virtual quarks which comprise the strong nuclear force.

This

feature is shared by the neutron and the proton, which

differ only in regard to the

udd

and

d valence

quarks which respectively provide the nucleons with their net quantum

numbers. Since the

and

quarks in question have masses of just a few MeV, it is no

longer particularly surprising that the neutron

-proton mass difference is also of this o

rder.

In fact this is to be expected. The moral is that there are structural reasons why the

neutron and proton masses should be very close. This is not to say that there is no

tuning at all, just that it is not so terribly fine as it first appears. It

is more indicative to

compare

pn mm

with the mass of the electron or the mass of the

quarks. On this

cale the tuning is at the level of tens or hundreds of percent, rather than less than 1%.

Nevertheless, there is some

tuning. For

example, the

quark must be heavier than the

electron for atomic stability

In E

xample

(ii), the neutron:proton ratio

depends upon

, the temperature when the

leptonic reactions which interconvert neutrons and protons are frozen o

ut by cosmic

1 The term biophilic will be used here to refer to a universe which is sufficiently similar to our universe

that conventional biochemistry could potentially arise. Biophilic universes are therefor

e a sub

set of all

complex universes (probably a very small sub

set).

That is, if we make the rather sweeping assumption that

udpn mmmm

. Far more carefully

argued constraints on the

u, d

and

s quark masses which produce a congenial unive

rse have been

discussed recently by Jaffe, Jenkins and Kimchi [31] and by

Damour and Donoghue [19]. The term

congenial is defined in Jaffe et al as universes with quark masses which allow for certain key nuclei to be

stable (so as to make organic chemist

ry possible).

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

expansion. This freeze

-out temperature depends upon the strength of the weak nuclear

force, G

. Because the neutron:proton ratio is

mm pn /

exp

, i

t is often claimed

that it is highly sensitivity to changes in the freeze

out time, a

nd hence to the strength of

the weak force. Actually, a closer examination shows that if the Fermi constant, G

were

reduced by an order of magnitude, the universe would still be 18% hydrogen (by mass, or

~50% by number of atoms). This would still support hydrogen burning stars with lives in

the order of billions of years, long enough for biological evolution. Reducing G

by a

factor of 100 would still leave the universe with ~14% hydrogen by number of atoms.

Admittedly if the hydrogen abundance were reduc

ed too much this would ultimately

prejudice the formation of the first stars, which is believed to rely on a cooling

mechanism

via molecular hydrogen.

Nevertheless, there is no obvious reason to regard as

catastrophic a reduction in G

by somewhat more tha

n a factor of ten.

Moreover,

the constraint on G

only

single

sided: it must exceed

(say)

~10%

its

actual value

but there is

no obvious upper bound resulting from these considerations.

were increased, then there would be less helium in the uni

verse. For example, a factor

of 4 increase in G

results in only ~0.2% hel

ium by mass. But this would seem

unimportant. Helium appears to play no essential role in the formation of large scale

structure or stellar physics

3. Although no upper bound on GF

sults from these

considerations, there are suggestions that Type II supernovae require GF

to lie close to its

actual value. This is because crucial aspects of the mechanism of Type II supernovae

involve neutrino interactions, i.e., weak

force interactions.

The neutrinos seem to be

required to interact just weakly enough to escape the core of the collapsed star, but

strongly enough to transfer

sufficient

energy to the mantle to cause the explosion.

Unfortunately the quantitative understanding of Type II supe

rnovae is too poor to deduce

just how fine tuned G

must be.

Hence

there is a case for considering G

to be a genuine instance of tuning, but it is not

necessarily terribly fine

, and may only be single

sided

Example (iii)

, deuteron stability,

does app

ear to provide a genuine instance of fine

tuning, requiring g

to exceed ~85% of its actual value. Claims are often made that there

is also an upper bound on g

to avoid diproton stability. If g

were ~10% larger, then the

diproton (

) would be a bound state

. It has frequently been claimed that this would

lead to an all

helium universe. The argument is that all the nucleons would end up as

helium during BBN, either via the conventional sequence starting with

Hpn 2

via the diproton

5 eH

pp 2

. However, this argument is just wrong. The

reason is that, even if the diproton were stable, the rate of its formation via

pp 2

is too slow for any significant number of diprotons to be formed

during BBN

, [12

]

. It is

The ppII and ppIII reaction sequences would be slowed by the absence of initial helium, but the ppI

sequence is unaffected.

The diproton is not bound in this universe. This is because the spin

singlet nuclear force is weaker than

the spin

triplet nuclear force which binds the deuteron. It is

not

, as some authors have claimed, due to

electrostatic Coulomb repulsion.

The inverse beta decay which converts the diproton to a deuteron is possible because the binding energy

of the deuteron (2.2

24 MeV) exceeds

epn mmm

1.804 MeV.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

true that the nuclear physics of stars would subsequently be very different, but there is no

obvious reason why biophilic stars would not be stable

, [12

There is possibly a different upper bound on g

. If g

were increased suffi

ciently that

deuterium were stable even at the higher temperatures prevailing before 1 second, when

the leptonic reactions were still active, then the nucleons could escape into the sanctuary

of helium

4 before the protons had gained numerical superiority

over the neutrons. This

would again lead to a universe with little hydrogen. However, rough estimates suggest

that g

would need to be increased by more than a factor of two for the hydrogen

abundance to fall to potentially abiophilic levels.

Hence, deuter

on stability

provides

a case for fine tuning of g

(a lower bound of ~85% of

its actual value)

but

any upper bound

arising from BBN

is rather generous in magnitude.

Example (iv) concerns

the famous Hoyle [

]

coincidence.

The instability of beryllium

(

4) means that carbon ( C

) can be produced only by virtue of the subsequent alpha

capture reaction

being extremely fast due to the existence of a

resonance of the carbon nucleus at just the ri

ght energy. Moreover, the subsequent

burning of all the carbon into oxygen is avoided

only

by the fortuitous placing of the

energy levels of the oxygen nucleus so that resonance is just avoided.

Some authors are

not impressed by t

he Hoyle

coincidence

for

example, Weinberg

[53

]

But actually

quite elementary arguments based on first order perturbation theory are sufficient to show

that Weinberg s objection does not stand up to quantitative scrutiny. The triple alpha

resonance energies with respect to the

ir reaction thresholds are highly sensitive to

changes in the strength of the nuclear force

A mere 0.4% change in the strength of the nuclear force can produce a change in the C

sonance energy of up to 38%, [17,18,

]

. C

onsideration of the detailed stellar

models reported in these same references suggests that a reduction in the C

resonance energy of perhaps ~50% will result in a reduction in carbon production of

around two orders of magnitude. A

lternatively, an increase in the C

resonance

energy of ~50% will result in a reduction in oxygen production of around two orders of

magnitude. These changes in resonance energy would be brought about by a change in

the strength of

the nuclear force

not exceeding +

respectively.

Consequently it appears that the Hoyle coincidence is impressively fine tuned, requiring

changes in the strong force of less than ±1% to challenge the likelihood of conventional

biochemistry by ser

ious depletion of either carbon or oxygen

abundance. However, this

fine

tuning might only be one

sided. The reason is that an increase in the nuclear force of

6 Weinberg, [40] says, I don t set much store by the famous coincidence emphasised by Hoyle, that there

is an excited state of C

with just the right energy to allow carbon production via

reactions in

stars. We know that even

even nuclei have states that are well described as composites of

particles. One

such state is the ground state of Be

, which is unstable against fission into two alpha particles. The same

potential that

produces that sort of unstable state in Be

could naturally be expected to produce an

unstable state in C

that is essentially a composite of three alpha particles, and that therefore appears as a

low

energy resonance in

reactions.

So the existence of this state doesn t seem to me to provide

any evidence of fine tuning

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

less than 1% will make

stable. The triple alpha reaction, via the resonant states

and

, would then no longer be necessary. Ins

tead a star might

accumulate

macroscopic quantities of

and synthesise subsequent elements in a more

conventional manner.

Whether the res

ulting nuclear physics and stellar physics would

render this a feasible pathway for biophilic carbon and oxygen production is difficult to

judge.

It is concluded that the Hoyle coincidence is an instance of fine tuning, requiring that the

nuclear force ex

ceed 99% of its actual strength. It may also need to be less than 101% of

its actual value, but this is less clear.

In summary,

whilst the tuning of some universal constants may not be as numerically

impressive as is sometimes claimed, and might only be

single

sided in some cases,

nevertheless tuning is evidently a feature of the world.

2.2 Varying Multiple

Parameters

Alternative Complex Universes

In section 2.1 we have been guilty of giving the impression

that fine tuning requires

the

affected univer

sal constant to

lie within a certain range of values. Indeed many

discussions of fine tuning give this impression. But this is quite wrong. In fact, all

instances of fine tuning provide relations between

two or

parameters

. Examples are

as follows,

Con

sider the bound on th

e neutron mass

discussed in section 2

. Algebraically this

Bmmmmm epnep

where

is the

difference in

binding energy

between

the

nucleus in question

and the nucleus obtained by replacing

So the

llowed range for the neutron mass depends upon the other masses, which in turn

depend upon

the quark masses

and other constants of the standard model.

educing the weak coupling constant, G

sufficiently could challenge

the

preservation

of hydrogen during

the Big Bang

. However, the excess of protons over

neutrons at the time of the freeze

out of the leptonic reactions depends upon the

product

FmmG 3

, so that a reduction in G

can be compensated by an increase

in the nucleo

n mass difference. (This is likely to involve a reduction in the neutron

lifetime, which also influences the final proportion of hydrogen surviving the Big

Bang, but the photon:

baryon

ratio can be re

tuned to negate that effect if necessary).

The lower bo

und on the strength of the nuclear force, g

, to bind the deuteron was

stated in s

ection

2.1

actual

ss gg ,

. But closer inspection reveals that the range

of the nuclear force, and the nucleon mass, are also part of this calculation. The

combina

tion of parameters which is bounded below is actually

mmg ns /

, where

is the pion mass. So the numerical bound on

gcan be changed by varying the

nucleon:pion mass ratio.

The stability of large nuc

lei requires that the quantum of charge is not too great or

else the Coulomb repulsion between the protons will blow the nucleus apart. But a

larger quantum of charge can be compensated by also increasing the strength of the

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

nuclear force. This produces an

inequality involving both

and

, the

electromagnetic fine structure constant.

One of the original f

ine

tunings of Carter [15,16

] was the requirement that small stars

be convection dominated whilst large stars be radiation dominate

d. This leads to the

coincidence

. This is a statement about the relative strengths of the

gravitational and

electromagnetic forces and involves several constants

Since all known examples of parameter sensitivity are relations betw

een two or more

constants, it is clear that each such individual relation can at best give a constraint like

that illustrated in Figure 1.

Note, however, that there will be many constraints like Figure

1 which must be satisfied simultaneously, potentially

up to one for each case of fine

tuning.

The intersection of these separate constraints might

restrict

individual parameters

more narrowly

ee Figure 2 of Bousso et al [

9]).

Figure 1

Illustrating a logical fallacy: the observ

ation of fine

tuning in parameters c

and c

does not imply that they are confined to the red dashed box.

The lesson that can be learnt from t

his simple observation is that complex

universe

might result for values of the universal constants which depart g

reatly from the usually

claimed fine

tuned bounds, p

rovided

that

the parameters

remain

the complex

region

i.e.,

between

the bounding curves in Figure 1. Radically different, but still complex,

universes may exist in these directions

in parameter spac

. Support for this contention is

provided by a number of radically different model universes which have been constructed

And they will all exhibit parameter sensitivity

see section 5.

Fine tuning is observed in

both the parameters c

and

, as indicated by the

arrowed lines. However, it is

incorrect to conclude that the

constants are ther

efore

restricted to the box

indicated by red dashed lines

Actually, a complex universe might result

for any (c

) lying between t

he two curves.

This may include points (c

) which lie far

from the values in this universe

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

Aguirre [4

], by

Harnik, Kribs and Perez

[27

], by Adams [1] and by

Jaffe, Jenkins and

Kimchi

[31

These are summarised in turn.

Aguirre s Cold Big Bang Universe

On the basis of considering the effect of single parameter variations on struct

ure

formation, Carr and Ress [13

] have argued that

the photon:baryon ratio

cannot be

less

than ~10

6 . Similarly

, Tegmark and Rees [

] argue tha

t the magnitude of the primordial

density fluctuations, Q, is fine tuned to be within an order of magnitude of its value in

this universe. Despite these parameter sensitivities, Aguirre [4

] has presented a case for a

universe

potentially

capable of support

ing life in which the photon:baryon ratio

, ,

is of

order unity, and Q is smaller than its value in this universe by a factor of between a

thousand and a million. Aguirre argues that such a cosmology can produce stars and

galaxies comp

arable in size and longevity to our own. As a bonus, a rich chemistry,

including carbon, oxygen and nitrogen, can arise within seconds of the Big Bang.

The

previously claimed single-

parameter bounds on

and Q are avoided by varying b

oth at

once

, and by many orders of magnitude

The Weakless Universe of

Harnik, Kribs and Perez

(HKP)

Harnik, Kribs and Perez [27

]

consider a universe which has no weak nuclear force. This

is achieved by HKP by simultaneously varying the parameters of the s

tandard model of

particle physics and the cosmological parameters.

Section 2.1

discusses

how reducing the

value of the Fermi constant sufficiently would lead to a universe with insufficient

hydrogen to support familiar c

hemistry. The reason is that a

small

er G

produces an

earlier

freeze

out of the leptonic reactions

. He

nce the

temperature is

higher and the

abundance

of neutrons and protons

are closer to equality

. However, we have taken for

granted that the neutrons and protons achieve their thermal equilibrium densities. This

will only be the case if the weak interaction exists, since this provides the mechanism for

the

inter

conversion. Thus, the situation is entirely different if the weak interaction is

effectively absent in the hadron era.

In this cas

e, HKP

assume that

the relative neutron

and proton abundance

can be fixed

fiat

, as can the photon:baryon ratio.

HKP

found that they could contrive a universe with a similar hydrogen:helium ratio as

ours, but with about 25% of the hydrogen being deuteri

um rather than protons. To do so

they

chose a photon:baryon ratio of 2.5 x 10

, i.e., about a

hundred times larg

er than in

our universe. HKP argue that galaxies could still form despite the much reduced visible

baryon density, but that the number density

of stars in the galaxies would be

appropriately reduced. They can claim that stars would form, because they have taken the

precaution of making the chemical composition of their universe sufficiently similar to

ours, thus ensuring that there would be a coo

ling mechanism to permit gravitational

collapse.

In the HKP universe the initial fusion reaction in stars would be the formation of helium

3 from a proton and a deuteron. Note that HKP have cunningly contrived to have

substantial quantities of deuterium f

ormed during BBN, so there is no need for the usual

weak

force

mediated deuteron formation reaction from two protons. Since the first stellar

reaction in HKP stars is very fast compared with the usual weak

mediated deuteron

formation reaction, the core tem

perature of such stars would be lower. It has to be lower

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

to keep the reaction rate down to a level at which the thermal power does not outstrip the

available mechanisms of heat transport away from the core.

The moral of bo

th Aguirre's

and HKP s model uni

verse

is that by varying more than one

parameter

at once, and by being bold enough to vary them by many orders of magnitude,

it is

possible to discover distant regions of

parameter space which potentially could

support a complex

universe

with a rich chemi

stry

. The key is varying more than one

parameter

at once. Consistent with Figure 1, the change in one parameter effectively

offsets the change in another. In addition, by making very large changes, the nature of the

physics involved changes qualitatively.

Adams Parametric Survey of Stellar Stability

Adams

] has considered how common the formation of stars might be in universes with

different values for the universal constants. T

he most important quantities which

determine stellar properties are the grav

itational

constant G, the fine structure constant ,

and a composite parameter that determines nuclear reaction rates. Adams uses a simple

analytical model to determine the region within this 3-

dimensional parameter space

which permits stellar stability

. Using a pa

rameterisation based on the logarithms of the

above constants, Adams concludes that about one quarter of the region defined by either

increasing or decreasing G or by ten orders of magnitude supports the existence of

stars. Whilst this cannot

easily

be t

ranslated into a statement about probabi

lity

nevertheless

the requirement that stars be stable is hardly a strong constraint on the

universal constants

a dramatically differen

t conclusion from Smolin s [

]. Yet again,

so long as more than one parameter

is varied,

the universe can evolve

complexity

(in this

case, stars)

even for parameter values very different from our own.

The Modified Quark Mass Universe of Jaffe, Jenkins and Kimchi (JJK)

Another

set of

example

s of potentially biophilic alternative

uni

verse

, obtained by

varying more than one parameter,

has been offered by

Jaffe, Jenkins and Kimchi

[31

-33]

In these examples the parameters which are varied are the masses of the three lightest

quarks,

u, d, s

, together with the QCD scale,

QCD

. JJK consider, for example, a universe

in which the proton would be slightly more massive than the neutron. Whilst atomic

hydrogen would then be unstable, they argue that deuterium and tritium, as well as some

isotopes of carbon and oxygen, could

be made stable. It is feasible, therefore, that a rich

chemistry could emerge in such a universe. A more radical alternative considered by JJK

to reduce the strange quark mass considerably, so that nuclei become bound states of

neutrons and

rather than protons. Again JJK argue that some isotopes of hydrogen

and the surrogates of carbon and oxygen would be stable

and would be expected to

possess comparable chemistry. What would happen to stellar physics in these universes,

and wh

ether the required elements would actually be formed in abundance, is unknown.

But t

hese examples again demonstrate

the potential for complexity to arise if multiple

parameters are varied to a congenial part of parameter

space

(using the term congenial

s JJK use it)

It will be demonstrated below

that all

alternative universes

which give rise to complexity,

such as those suggested by Aguirre, HKP, Adams and JJK,

will

inevitably display fine

tuning.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

The Two Distinct

Fine Tuning

Phenomena

How fine is f

ine tuning? The examples considered in section 2.1 support the existence of

some degree of tuning, but the fineness is more debatable. Biophilic abundances of

carbon and oxygen appear to require g

to be fine tuned to within

, and nu

clear

stability requires the neutron mass to be fine tuned to within

%1/%

assuming a

fixed proton mass.

These cases seem quite fine , b

ut the latter example is largely, but not

completely, explained by the nucleon structure.

Klee [35

]

has point

ed out that many of

the commonly

cited fine tunings are actually not at all fine, and even claimed

order

magnitude tunings

are stretched to cover several orders of magnitude.

The survival of primordial hydrogen may be an example, since F

could accommodate

an order of magnitude reduction without hydrogen abundance being too greatly

diminished. On the other hand,

in a universe in which the gravitational and electrostatic

forces between two electrons differ by 42 orders of ma

gnitude, perhaps a mere factor

ten would count as reasonably

fine tuned?

are

interested in the d

egree of fineness of the tuning? It is

because the finer the

tuning

the m

ore remarkable

the coincidence

or s

o one is tempted to think. But

actua

lly the intuitive notion that a very fine tuning translates into a small

a priori

probability is hard to defend.

A number of authors have pointed out that

the smallness of

the numerical window within which a parameter must lie says nothing at all about its

probability (e.g.,

Manson [38], McGrew et al [40

]).

Since

a probability measure

parameter space

is not available this is hard to dispute.

However, the pragmatic approach of this paper is that examples like those of section 2.1,

and others in

[2,3,6,7,1

16,20

24,26,28,29,

], do illustrate a real tuning

phenomenon which requires explanation. The degree of tuning may be fine (a few

percent or less) or not

fine (perhaps an order of magnitude), but the latter is no less in

need of an explanation

for

being coarse

tuning

. Both may be regarded as small parameter

windows

, in some context

. And the fact that neither can strictly be claimed to be

improbable is not pertinent.

It is not the probability that we seek to explain, but the

examples of tuning illustrated in section 2.1 and in [2,3,6,7,13-

16,20

24,26,28,29,46,47].

An explanation is required for both fine and not

fine tunings. To avoid clumsiness of

exposition, we continue to use the phrase fine tuning to mean both fine and relatively

coarse tunin

gs.

We contend that fine tuning actually consists of two distinct phenomena.

The first phenomenon is the parameter sensitivity of the universe. This is the (apparent)

property of the universe that small changes in the parameters of physics produce

catast

rophic changes in the evolved universe. In particular the complexity of the evolved

universe, and hence its ability to support life, wo

uld be undermined by

small changes in

the universal constants

(in the pragmatic sense of small changes

discussed above)

Thus, parameter sensitivity is the claim that the target in parameter space which is

compatible with a complex universe is small

in some sense. The smallness of this

target,

if true, is

a feature

which requires explanation.

The second, and quite disti

nct, p

henomenon

that

nature

has somehow managed

to hit

this small target

which we will refer to as fine tuning

. T

he actual constants in our

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

universe

have to

be fine tuned to coincide with the requirements for a complex outcome.

In other words, given

that only special values for the parameters will do (i.e., given

arameter sensitivity),

nature

had to

contrive to adopt these particular values (i.e.,

nature

is fine tuned).

The present paper is concerned only with the first phenomenon: parameter sensiti

vity and

how it arises.

A great deal has been written about

the merits, or otherwise,

some sort of

ultiverse

the

contrivance by which the small target

in parameter space

is successfully

hit

(i.e., fine tuning is achieved).

It seems to have gone larg

ely unnoticed that an

explanation is

also

required of

the distinct phenomenon of

parameter sensitivity

The

Multiverse

postulate does not

even attempt to explain

parameter sensitivity, i.e.,

why the

target is small in the first place.

So, why

is the univer

se parameter sensitive

There is a danger of misunderstanding

this point. Physicists might

argue that every

instance of fine tun

ing

(e.g., those listed in section 2)

constitutes a demonstration, via

physical calculation, that the target is

small. They migh

t opine that the question why

parameter sensitivity? is answered by the totality of such calculations.

But our

calculations are merely observations that parameter sensitivity appears to prevail in

our

universe. They do not provide an explanation of why t

his should be so

, i.e., why this

feature should be expected

The

point can be illustrated in the following way. Before one looks into the physics of

these things, it is not obvious

that there could not be complex universes corresponding to

the bulk of the

volume of parameter space. Take life as an exemplar of complexity

and

onsider the universes which might result if gradual

changes were made to the universal

constants

We can imagine, wit

hout any nonsense being obvious

, that

the

life

forms of our

universe

might give way to a continuous spectrum of morphing lifeforms as the physical

parameters varied. Eventually radically different lifeforms would emerge, living in a universe

whose physics was also radically

different

. B

his description of the consequenc

es of

changing the universal constants is precisely what parameter sensitivity claims is

not

true.

But why is this?

Specifically,

why could this never

be true in any universe which evolves

complexity

This is the question addressed in the following section

We shall argue that p

arameter sensitivity

mathematical

result of the

assumed

emergence of complexity

We shall argue that parameter sensitivity

is inevitable in any

complex universe

, and hence, as a consequence, so is fine tuning.

How Parameter S

ensitivity Relates to the Evolution of Complexity

: Toy Models

his section illustrates, with the aid of toy models, the way in which parameter sensitivity

arises from the assumption that the universe evolves complexity.

What is meant by a complex universe

? This is a difficult question, so it is fortunate that a

complete answer is not required for the present purposes. We shall see that conditions

which are clearly necessary for the emergence of complexity turn out to be sufficient to

imply parameter sensit

ivity.

In considering the meaning of a complex universe we generally think of the universe as

it is now. The living organisms and the ecosystem of planet Earth are the epitome of

complexity. However, all this did not emerge fully formed in a single step

from the

fireball of the Big Bang. Rather it is the current state of (one part of) a universe which has

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

been evolving for 13.7 billion years. The history of the universe is one of increasing

complexity

, [

24,41,45

]

. Thus, the formation of helium nuclei aft

er the first few minutes

represents an increase in complexity compared with what preceded it. The same is true of

the formation of the first neutral atoms at ~360,000 years, and the first stars or galaxies at

some hundreds of millions of years. The gravita

tional congealing of matter provided the

opportunity for complex, orderly structures to arise. Despite their gaseous form, stars

have a considerable complexity of structure and evolution. The structure of galaxies is

vastly more complex still, acting as they do as stellar nurseries. And the solid

ast

ronomical bodies, planets

and asteroids, provide the opportunity for great complexity

on smaller size scales.

From the point of view of the se

cond law of thermodynamics it initially appears curious

that the

Bang fireball, which is generally

assumed to have been in local

thermal

equilibrium,

nevertheless gave rise to a universe which spontaneously produced orderly

structures

. This comes about because the orderly, and complex, structures occur in

regions of gr

avitational collapse. Such regions have shrugged off their excess entropy,

using the vast tracts of almost empty universe as a dumping ground. This is the salient

fact: inhomogeneity of the entropy distribution is a necessary condition for the emergence

complexity.

This world was not always complex. It became complex.

And because, at the

fundamental level, becoming necessarily entails dynamics, t

he complexity of the world

is a product of dynamics

. Most

especially

the dynamics of gravitational collapse

and

nuclear fusion are the root cause of the

possibility

of complexity

Both of these processes

lead to the reduction of the entropy of (a part of) the baryonic component, the excess

entropy being carried away by other, generally lighter, particles, e.g.,

photons and

neutrinos.

And when complexity reaches the level of life, it is sustained against the

tendency to increase its entropy (decay) by the flux of free energy from its parent star,

Egan

[25],

Lineweaver

and Egan

[

Michaelian [

Wallace [

It may be unusual to speak of stellar nuclear reactions as dynamics , but the

reacting

core of a star is comprised

a myriad of

individual particle d

ynamics.

So if complexity

emerges from dynamics,

and

parameter sensitivi

ty is defined in reference to

complexity,

it follows that parameter sensitivity should

also

be understood as a property of dynamics.

Fortunately

thermo

dynamics, the statistical properties of many body dynamics, suffices.

The key is to recognise that only a s

mall portion of the mass

the universe will end up

complex.

We do not need to consider the whole observable universe, but just some

comoving region

, which is large enough to approximate to a closed s

ystem

Within

the sub

-system which will end up complex will be called .

It is necessarily an

open

sub

system and

may be regarded as a fixed inventory of baryonic matter.

It is claimed that the

sequence of processes leading to complexity must include steps in which

reduces its

entropy and hence becomes more ordered.

We claim that this is sufficient to produce

parameter sensitivity.

Note that, in accord with the second law of thermodynamics, the

entropy of

can only i

ncrease

In fact, the irreversible processes involved in forming

and sustaining

implies that the entropy of

will

increase.

The relationship between entropy and complexity is not an easy one. It is certainly not the

case that unfettered entropy minimisation leads to complexity. Arranging atoms in a

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

perfect crystal structure minimises their entropy but is the antithesis of complexity. On

the other hand, the maximal entropy of a gas in thermal equilibrium is also the ant

ithesis

complexity.

These observations are consistent with the contention that c

omplexity

appears to exist

at the boundary between order and disorder (

Prigogine [

Kauffman

). Many definitions of complexity have been offered, but there is no univ

ersal

agreement. Fortunately the only claim we need make is that some of the evolutionary

steps, starting from a universe devoid of structure, must involve the reduction of the

entropy of

If true complexity is to be the outcome, th

en such processes will not

proceed to minimisation of the entropy of , since, as noted already,

would not then

be complex. Nor is it necessary for the reduction in the entropy of

to be m

onotonic.

certain number

of entropy reducing processes is claimed to be necessary, but certainly not

sufficient, for the emergence of the highest degrees of complexity.

Our

contention is that this ho

lds for

any set of universal constants

, and any replac

ement

of the standard model of particle physics,

which result in a complex outcome.

A simple toy model will help illustrate a sequence of entropy reducing steps.

deliberately choose

a form of particle physics whic

h differs from the standard model

ord

er to emphasise the generality of the argument. However, it reads across t

o similar

processes in our

universe.

Let us suppose that complex structures are to be built out of combinations of two types of

matter particle:

and

These particles are assum

ed to be present in a free state in some

primordial, chaotic epoch of the universe. The first step in reducing the entropy of the

matter component of the universe may consist of a reaction dcba

, where

is to

be regarded as a bound sta

te of

and

. The reaction is assumed to be exothermic.

lmost all

the rest mass of

and

ends up in

, whilst particle

is relatively light and

hence will carry away the bulk of the energy released. So a

and

are the analogues of

baryonic matter,

whereas

may be

the analogue of a photon

or neutrino

. The reaction

produces a reduction of the entropy of the baryonic matter simply because, if attention

is paid to the baryonic components alone, the reaction is

cba

. So one particle

results

where there were previously two. Other things being equal, entropy becomes simply

particle counting, so this represents a reduction in the baryonic entropy

by a factor of

about

Of course the reaction proceeds because it causes an

increase

in t

he total entropy of the

universe. There is no deficit in the number of

all types of

particle in the reaction

dcba

. Moreover, the energy released leads to an entropy increase. The energy

released by the reaction is the binding energy,

Bc,

and

b in the bound state c

. For the

reaction to make net progress in the face of potential thermal dissociation (i.e., despite the

reverse reaction

badc

), the binding energy must be large compared with the

typical prevailing therma

l energy,

. Hence the energy of the photon , d

, is

much larger

than

. Presuming that these

particles have some mechanism available by which they

can come into thermal equilibrium with the surroundings, it fol

lows that after

thermalisation the initial energy of the

particle will be spread over

1/~

different particles.

Increasing the energy of a large number of particles constitutes

entropy increase. In summary, the reduction of the bary

onic entropy is bought at the cost

of an overall increase in entropy which is born by the other particles (e.g., particles

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

Any reasonable measure of the strength of the interaction which causes the binding of

and

will be such that the binding ener

increases monotonically with the strength.

Hence we can use

itself as a measure of t

he strength of this interaction

. The reactio

will proceed only if the interaction

is strong enough to overcome thermal dissociation,

which we can write symbolical

ly as

(whilst accepting that there will really be

phase space factors and so on which complicate the exact expression). There is nothing in

the least surprising about this: the interaction must be strong enough to make the reaction

o. But note that

is a constraint on the universal constant , c

, which measures

the strength of the interaction, and this constraint is necessary in order to achieve a

reduction of the baryonic entropy via dcba .

This is

an example of how entropy

reduction of

results in a constraint on the universal constants, and ultimately parameter

sensitivity.

Our toy model has not yet achieved any significant complexity, and could

not be

expected to do so in a single step

. A succession of entropy reducing steps of differing

kinds is to be expected, and a complex outcome must at least include a great diversity of

compound particles. So we suppose that subsequent reactions can occur

hich result in

compound particles of the form

mn ca

. We may write this as

being understood that this is shorthand for a sequence of two

body reactions. There are

light particle

, which carry

away the bulk

of the binding energy released in forming the

composite particle

mn ca

. For the same reasons as before, such a reaction involves an

overall increase in entropy, as it must, but a reduction in the baryonic entropy

because

particles are replaced by just one compound baryonic particle. Also for the

same reason as before, the interaction which binds the compound particles

mnca

must

have a certain minimum strength to overcome thermal dissociation (the re

verse reaction).

However, there is now an important additional feature. Reactions of the form

can occur only if the initial reactions

dcba

do not consume

all the

particles.

But this leads

to an

upper bound

on the strength of the interaction

measured by

, in addition to its lower bound established previously. This can be seen

as follows.

Firstly l

et us assume

that

dcba

is far faster than

. If

dcba

were to proceed to completion, reactions

could not

occur. For

to occur, t

here

would need to be some

means of

terminating the

dcba

reactions whilst s

ome

particles remain

This may

arise

due to

dcba

being frozen

out by falling temperature or by cosmic expansion. Or

it may be that some other reactions are also occurring which result in copious production

particles. A very large density of

particles will favour the reverse reaction

badc

and might lead to a dynamic equilibrium at some non

zero density of

particles.

Whatever the mechanism, a non-

zero density of

particles can result only if

the strength of the

interaction

B, is insufficient to drive the reaction against the

countervailing effects.

For example,

dcba

would be frozen

out by cosmic

expansio

n if the reaction rate falls below the universal expansion rate (i.e., the Hubble

parameter). But the reaction ra

te will increase if

the interaction strength,

were

increased

. So freeze

out whilst a reasonable abundance of

particles remains requires

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

that the interaction strength,

is less than some bound. Too large a value for c

would

result

in a late freeze

out, when the

particle density had already fallen too far.

Secondly, what happens if we assume that

dcba

is far

slower

than

? In this case the burden of achieving a balance of compound

particles

mnca

shifts to the relative rates of

the various reactions implicit in the sequence

leading to

. We shall see in the toy model below that this also

requires the interaction strength,

, to be bounded both above and below.

And finally, what if we ass

ume that the rates of

dcba

and

are comparable? Well, in that case, we have assumed fine tuning from the start

namely

that the strength of the interaction driving the first reaction is closely matched by the

stre

ngth of the interaction driving the second.

there is an upper bound to

as well as t

he lower bound established previously

. Only

if the strength of the force is bracketed between a lower and an upper bound can both

reactions

dcba

and

actually happen. This is the origin of

parameter sensitivity, as illustrated by Figure 1, for this illustrative example

The point is that parameter sensitivity

(in the sense of a parameter being bounded both

above and below) i

s necessary in order

that the baryonic matter can undergo

sequential

entropy reductions through both

dcba

and

mn .

The upper and

lower bounds are

both

required in order to produce the compound particles

mnca

he prize is to

achieve a rich variety of suitable chemistry, not merely a monoculture of

single nuclear variety

our universe, nucleo

synthesis

in stars

enriches the ISM with

very b

road range of nuclei in several

ways. Some lighter nucl

ei are ejected as the star

evolves, in the form of stellar winds and various instability phenomena.

fully evolved

stars,

elements up to

iron are preserved by the shell structure in which there is a gradation

of temperature, pressure and density conditio

ns.

Finally, elements beyond iron are made

by the complex physics occurring during supernovae.

It is not trivial to e

nsur

a balance

of this kind in the abundance of the products of nucleosynthesis

In our universe, the synthesis of the chemical element

s inside stars is immensely

complicated.

to illustrate how the production of a balance of elements requires fine

tuning we

opt for a

simple toy

model

. We return to

Gamow s original idea

in which

the

chemical elements are made during

BBN

. To permit this to happen we change particle

phy

sics and nuclear physics

drastically.

There is no neutron in this

universe;

the only

nucleon is the proton.

Protons in this universe

can form bound states of two, three, four,

and up to ten nucleons via some

analogue of the

trong nuclear force

The

time

temperature relation is assumed equal

to that in our universe.

The nuclear

reaction rates

are

contrived

to give the more highly charge

nuclei a reasonable chance of being

formed, despite the falling temperature and density.

This means radically altering the

Coulomb barrier (by

fiat

, there is no underlying theory here). The strength of the nuclear

force is measured by the binding energy per nucleon,

, which is assumed to be the same

for all nuclei.

The absolute number densit

y of nucleons is found from an assumed photon:baryon

ratio,

, and the usual black

-body photon density in terms of temperature. The absolute

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

number densities are also adjusted due to cosmic expansion following the usual time

dependence

The reaction network consists of 25 different reactions. These reactions are

eventually frozen

out by cosmic expansion.

e parameters

and

are the universal

constants whose fine tuning we wish to demonstrate.

The specific algebr

aic and numerical assumptions of the model are given in the

Appendix, and are essentially arbitrary.

It is rather obvious what the outcome will be. If

the fusion reactions are sufficiently fast compared with the cosmic expansion rate, the

reaction sequence

will proceed to completion before freeze

out. The universe will then

contain only the highest mass nuclei and no lighter nuclei. This will occur if either the

nuclear force is sufficiently strong (large

B) or the nucleon density is sufficiently high

(smal

). Conversely, if the fusion reactions are sufficiently slow compared with the

cosmic expansion rate, even the first compound nucleus (pp) will not have time to form

before freeze

out. The universe will be all hydrogen (

perhaps

perm

anently so i

this

universe remains star-

free

). This will occur if either the nuclear force is sufficiently weak

(small

) or the nucleon density is sufficiently low (large

Figure 2

Relative abundance

of nuclei for B=1MeV: Comparison of different

Relative Abundance of Nuclear Yields: Com

parison of

Different Photon:Nucleon Ratios for B = 1 MeV

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Atomic Number

Fraction of Total Nuclei

photon nucleon ratio 2x10^7

photon nucleon

ratio 10^7

photon nucleon ratio 3x10^6

photon nucleon ratio 10^6

photon nucleon ratio 3x10^5

photon nucleon ratio 10^5

photon nucleon ratio 3x10^4

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

Figure 3

Relative abundance of nuclei for

=106

: Comparison of different

Range of Binding Energy (B) producing Chemical Diversity

Versus Photon:Nucleon Ratio

0.001

0.01

0.1

100

1000

10000

1.00E+04

1.00E+05 1.00E+06

1.00E+07

1.00E+08 1.00E+09

photon:nucleon ratio

B (MeV)

lower bound of B for diversity

upper bound of B for diversity

Figure 4

Ranges of

B and (between the lines)

producing chemical diversity

Relative Abundance of Nuclear Yields: Comparison of

Differing Bindin

g Energies, B, for Photon

Nucleon Ratio 10^6

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Atomic Number

Fraction of Nuclei

B = 0.1

B = 0.3

B = 1

B = 3

B = 10

B = 30

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

The numerical results

of the model are in accord with these expectations, Figures 2 and 3.

The optimal balance of light and heavy nuclei is obtained for B = 1 MeV and 6

Suppose a chemically diverse

universe has at least a fraction 10

-4

of each element.

produce

such a chemically diverse

universe it is necessary that B and

fall within the

range shown in Figure 4. This is the realization of Figure 1 for this model.

Outside these

bounds the universe would be virtually all hydrogen

or virtually all neon (Z=10).

The

universal constants must

therefore

be fine tuned to produce a complex outcome

, i.e., a

diversity of chemical elements

. The tuning is not actually terribly fine, but then many of

the instances of tuning in our universe a

re not so terribly fine either.

Suppose we seek to circumvent this conclusion. We could make the fusion reactions very

rapid compared

to cosmic expansion, but protect the lighter nuclei from being consumed

in some way. For example, we could assume the pre

sence of some other type of particle

which could combine with protons or nuclei such that, after combination, the resulting

compound object was immune to further fusion reactions. Call this reaction X.

If reaction X is too fast

compared with the fusion re

actions

then we will end up with an

all hydrogen universe again. Conver

sely, if reaction X is too slow

we will end up

with

universe

containing

only the heaviest nuclei. So this contrivance fails: we will again

require a

fine tuning

relating

and

to whatever universal constant controls reaction X.

It will be apparent from these examples that the connection between parameter sensitivity

and a complex outcome is quite elementary in nature.

On the other hand, a few specific

examples

cannot establish the general truth of the assertion that parameter sensitivity is

always

a concomitant property of a universe which evolves complexity. This is addressed

next.

5 The General Dynamical Explanation of Parameter Sensitivity

We wish to

demonstr

ate that

any

sequence of entropy reductions of some subsystem,

must always require tunings of the

universal

parameters. Such a demonstration is

requi

red for any system of the

sort

consider

n the preceding examples

, in which

compl

exity is achieved by binding fundamental particles in ever more intricate ways. But

the proof should also accommodate any other form of entropy reduction, not just that

arising from particle binding. For example, volume contraction due to gravitational

col

lapse is a particularly important cause of entropy reduction in our universe.

Actually the demonstration should be more general still, since it is conceivable that

complexity could arise in quite a different manner. For example, structure

might not

reside

in binding

particles (i.e., in identifying their spatial degrees of freedom) but in a

correlation or coherence between spatially separated particles. Also, the fundamental

degrees of freedom may not be those of particles, but of fields. Most physicists be

lieve

that the number of field degrees of freedom is actually finite rather than a continuum,

limited to a spatial resolution at around the Planck scale. It is even possible (according to

the holographic hypothesis) that the resulting spatial lattice is on

ly two dimensional,

rather than t

hree dimensional, [11,

]. It is desirable to formulate the argument in terms

which are sufficiently general to embrace all these possibilities and more.

The natural arena for a generalised exposition is phase space. Phase

space comprises the

totality of degrees of freedom of the system in question, both generalised coordinates (or

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

fields),

, and generalised momenta,

. A point in phase space specifies a unique

microstate of the sy

stem. Studies of bulk behaviour consider, not individual microstates,

but macrostates corresponding to large numbers of possible microstates, and hence to

large volumes of phase space. For example, the pressure and temperature of a gas may

specify its macr

ostate, but there are many corresponding microstates, each of which

uniquely specifies the position and velocity of every molecule at a given time. The

volume of phase space within which a system might lie is a measure of the number of

possible microstates

, and hence is related to the entropy of the macrostate.

The evolution of complexity is thus related to the variation

over time

the phase space

volume occupied by

. Specifically, it is claimed that there are necessarily physical

processes which reduce the phase space volume

, since this

is equivalent to

reduction of the entropy of

Now the development over time of a given microstate

is described by

a trajectory through

phase space

. For deterministic physics, this trajectory is uniquely determined by the

initial state (the starting point in phase space) plus the physical laws

and

the values of the

universal constants. It follows that the development of the extended phase space regio

corresponding to a macrostate is also uniquely determined by the starting region, the laws

of physics and the universal constants, j

. In particular this applies to

It is

claim

that there must be processes wh

ich sequen

tially reduce the volume of the phase space

region

occupied by

. Suppose these processes are labelled 1, 2, 3 , in chronological

order. The phase space volumes of

at these times are

...

321 VVV

. But each

volume is calculable from the initial state for a given set of universal constants,

Taking the initial state and the laws of physics as understood, we can thus write

...

321 jjj cVcVcV . This is meant to emphasis

e that each phase space volume

can be calculated in terms of the assumed universal constants. This sequence of

inequalities between

calculable

functions of

c therefore implies constraints upon the

universal constants themselves. This

is the origin of parameter sensitivity.

It would not be reasonable to expect complexity to arise from a single physical process. A

sequence of processes is to be expected. The particular sub

set of universal

constants

which is important will

differ from o

ne process to another. So the sequence of processes

gives rise to different tunings, possibly of different sets of parameters.

It is important to recognise that the dynamics determines not just the change of volume of

the phase space region representing

but also its position within phase space. This is

crucial to the next process in the sequence. As we saw in the toy model above, moving to

a phase space region with no

particles may prevent

further

entropy red

uction. Hence,

the

path

taken by

through phase space is crucial. Achieving

sequential

entropy

reductions is a strong constraint upon the

global

path, not just upon the current process.

For example, the entropic benefit

of preserving hydrogen in the first minutes after

the Big Bang is realised only a billion years later with the formation of hydrocarbon

chemistry.

The phase space algebra can be made more explicit, and this has the advantage of

displaying t

he crucial path dependence more clearly.

For any deterministic physics the

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

phase space trajectory

txk

is uniquely defined by the initial microstate,

. This

statement can be written in differential form as,

jki

icxf

(1)

The functions

fspecify the physics which determines the system s evolution, and depend

both upon the current state,

txk

, and upon the universal constants,

We assume

that

the phase space is sufficiently generally formulated that it can address particle reactions.

Thus, if

dcba

occurs, the phase space includes regions representing both

and

Suppose, for c

onvenience of exposition, that significant physical events occur

at the discrete times

,...

,, 321 ttt

when the region of phase space occupied by

,...

,, 321

respectively. Consider a small

element of

volume of

at time

and

location

. A time

later the evolved system effectively defines a new

set of coordinates

iiii ftxttxx . The evolved v

olume

xdVd

is related to

the initial volume by the Jacobian determinant:

Vd j

And s

ince

we find that

to first order in

. Re

arranging

and integratin

g over the region

L yields the evolution of the phase space volume, L

corresponding to

, to be,

(2)

In the case of a conservative system defined by Hamiltoni

an mechanics, and if

were

replaced by the approximately closed system

the RHS of (2) would be identically zero

by virtue of Hamilton s equations8. Hence, the phase space volume does not change for

conservative

Hamiltonian systems (Liouville s theorem).

But, by hypothesis,

is a dissipative sub

system, necessarily ejecting energy and entropy

into its surroundings, so that its phase space volume

is reducing

. This is t

familiar behaviour of dissipative dynamic systems, whose phase space volume tends to

shrink asymptotically onto some attractor, typically of lower dimension than the phase

space (albeit probably fractal). Thus, the phase space volume

might shrink

asymptotically to zero.

In fact, the dimension of

will reduce each time

particl

es bind to

form composite baryonic particles

However, an equation like (2) will continue to hold

with the volume reinterpreted as b

eing

of reduced dimension.

8 The velocity field i

in phase space has ze

ro divergence because of Hamilton's equations.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

The entropy of

need not reduce monotonically. It is sufficient that there are times when

it does so. By definition, these are the times

,...

,, 321 ttt

Consequently our thesis i

s that,

cii

(3a)

cii

(3b)

cii

etc.

(3c)

In (3a

c) the dependencies upon the universal constants,

, have been explicitly

displayed. Not only do the p

hase space velocity functions,

, depend upon the

universal

constants, but so do

the changing phase space region

occupied by

over which the

integrals are carried out

. The path through phase space taken by the evolving region L

depends upon the preceding region from which it derives,

, and also upon the

physics encoded in the functions

, and also upon the universal constan

ts,

For

a conservative Hamiltonian system

, (3a

c) would be replaced by equali

ties. Moreover

these equalities

would be algebraic identities. But

(3a

c) are not algebraic identities. They

are dynamic constraints on any subsystem whos

e entro

py is successively reducing. And

note that all the dynamic variables,

, vanish from (3a

c) by virtue of the volume

integrations. Hence, (3a

c) are actually constraints on the universal constants,

, which

ust be fulfilled if

is to have sequential reductions in entropy. These constraints

constitute fine, or

possibly

not

fine, tuning.

These

relation

s are

the algebraic

embod

iment of Figure 1

The importance of the path,

L, taken through phase space must be emphasised. The path

determines the potential for continuing entropy reduction in later steps. The opportunity

for entropy reduction in, say, step 2, would be lost if step 1 resulted in a 2

which is not

conducive to further entropy reduction. A phase space path which permits continuing

entropy reductions over many sequential processes might appear highly contrived.

Indeed, it may

highly contrived. However, it is not our

concern here to exp

lain how

complexity comes about (i.e., how such a path may

arise spontaneously

). It is sufficient

to note that complexity requires this, and that relations like (3a

c) must follow.

This is the

origin of parameter sensitivity.

There are a number of potenti

al challenges to the generality of the above argument.

Firstly, it is possible to question whether (3a

c) do actually constrain the parameters

After all, if we replace

with the closed system

the second law of thermodynamics

tells us that,

)

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

and this must hold for

any

values of the parameters

. So, despite appearances, (4) is

not

a constraint upon j

. Why

should (3a

c) not also be of this type? To refu

te this

consider a

set of parameters,

, which correspond to switching off all

inelastic

interactions.

Under suitable circumstances t

he sub

system

can

now

be conside

red as

effectively

closed.

It is no longer exporting its entropy to

In which case we have,

)

But comparison of (3a

c) with (5) shows that (3a

c) clearly

constraint the parameters

since there is a set of values,

, for which (3a

c) are

not

true.

The second objection is that it is not entirely clear, in the general case, what is meant by

the distinct processes , enumerated above as 1, 2, 3

At the risk of being tautological,

these relate to the discrete fine tunings

. The limiting curve in parameter space which is

defined by the inequalities (3a

c) may be identified with what

Bousso et al [

9] refer to as

a catastrophic boundary .

The third ob

jection may be that not everything is dynamics . But actually, everything

that involves change

dynamics.

t may be unfamiliar to formulate some physical

processes in terms of dynamics

, simply because

the dynamic perspective may not be

helpful in perfor

ming calculations. But the physics underlying any change in any system

must be dynamical when considered at the microstate level. The formulation in terms of

phase space is a convenient means of linking the entropy reduction to the evolution as

determined

by the universal constants. It does not matter that it may not be a practical

means of carrying out a calculation.

The fourth

objection is the

assum

ption of

deterministic

(classical)

dynamics. This does

not address the potential indeterminism due to quant

um mechanical behaviour. However,

we are concerned with physics on an astronomical scale, with correspondingly large

phase space volumes. It is true that quantum calculations are essential in providing much

of the input to astrophysical calculations (e.g.,

reaction rates). However, there is no

compelling reason to be concerned that this translates into any significant indeterminism

at the scale of interest. As far as bulk behaviour is concerned, and providing we do not

attempt to address what happens at t =

0, it is likely that the classical formulation is

sufficient

to establish the principle

The final objection is that we have been cavalier in comparing phase space volumes

when the dimension of the sub

space occupied by

is reduci

ng. In a true continuum this

might indeed be a problem. But really

lking about phase space volumes is just a

shorthand for counting the number of degrees of freedom which are all ultimately

integers, whatever the dimension

may be

in the continuum desc

ription.

6 Interpretation

of Equations (3a,b,c )

in Our Universe

There is a danger that the v

ery generality of equations (3a,b,

) obscure what is actually

a simple message: every instance of fine, or not

fine, tuning in our universe is actually

an ins

tance of entropy reduction.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

Consider the examples of section 2.1. The fine-

tuned nucleon mass range (or

alternatively, the coarsely tuned quark mass range) relates

to nuclear stability, and hence

to the

potential for

entropy reduction via nuclear fusion.

The same applies to the lower

bound on the strong nuclear coupling of

he case of the Hoyle coincidence (the

production of biophilic abundances of carbon and oxygen)

is different. In this case the

entropy reduction does not occur a

t the time of stellar nucleosynthesis. Indeed, the star

would reduce its own entropy more if a long sequence of alpha capture reactions occurred

producing some very heavy nuclei, with little remnant carbon and oxygen. The entropic

benefit of biophilic prod

uction of carbon and oxygen,

to sub-

system

only

, occurs later

with the formation of organic molecules in the giant gas clouds and with planetary

formation and subsequent planetary chemistry. Similarly, the

constraint on the Fermi

cons

tant ar

sing from

survival of hydrogen during BBN does not reduce

entropy at that

time. The entropy

would be lower if the result

of BBN

were all helium. The benefit to

sub

system

is realised only with the formation of main sequence st

ars and with the

occurrence

of hydrocarbon chemistry after a billion years or so.

So the complexity

benefit of one of equations (3a,b,c ) may be long delayed, and is conferred on system

alone.

Whatever examples of fine (or coarse) t

uning are chosen, the relation to entropy

reduction can always be made. This is simply because all tunings are identified

as being

required

to permit

the formation of structure and complexity

and this implies entropy

reduction of the open sub

-system,

, in question.

But the complexity

benefit might occur

much later than the process giving rise to the numerical fine tuning.

For example,

Carter

[15,16] has argued that planetary formation is

facilitated due to

typical stars lying near

e boundary of convection and radiation dominance. This gives rise to the tuning

which, whilst derived from stellar physics, does not relate to

increased

complexity in the stars concerned. Instead the complexity

benefit

occurs only l

ater upon

planetary formation. Planets are system

in this case.

A further example is that,

in our universe

there must be stable stars to forge the chemical

elements beyond lithium.

The formation of stars requires a cooling mechanism

, this being

the mechanism by which entropy is exported away from the collapsing material

Assuming that

cooling is dominated by photon emission, this must require some lower

bound on the fine structure constant. Despite the fact that star formation is dif

ficult to

analyse algebraically, it is clear that cooling must require a lower bound on

since there

would be no cooling in the limit

. The lower bound on

is re

quired

both to

bring

about

the immediate entropy reduction of the collapsing

gas cloud

, and also to

ermit

the

formation

of the chemical elements

thereafter

The complexity

benefit of the formation of

the chemical elements occurs later still.

Where the above examples involve a

del

ayed

entropy reduction in system

, this

emphasises the importance of the path taken through phase-

space in the general

formulation of section

5. Thus, whilst equations (3a,b,c ) express our thesis in general

form, the interpretation

for any specific model universe is very simple.

Indeed it is

essentially merely a re

statement of the manner in which the fine tunings are usually

derived.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

Finally, what about fine, as opposed to not

very

fine, tuning? It is not clear wh

ether

equations (3

a,b,c

) produce particularly

fine

tuning.

But this does not matter. Equations

(3a,b,c

) are precisely the degree of tunin

g required to permit the associated

complexity

to arise. Whether this tuning happens to be fine or coarse is unimportant. Consequently,

referring back to section 3, we now see that it is inappropriate to be

overly

concerned

about the actual degree of fineness of the tunings evident in our universe.

They are as fine

they need to be.

Relation of these Observations to Other Issues

What

is and what is not explained

The hypothesis of this pape

does not address

how the universe becomes

fine tuned.

explanation

of parameter sensitivity

alone

has been offered, i.e., why the target in

parameter space is necessarily small.

No comment is

de regard

ing how the universe

contrive

to hit this small target.

The

existing

scientific

responses to this question have

involved one of the many variants of the Multiverse. The present work leaves these

offered explanations for fine tuning untouched, nei

ther supporting nor refuting

them

However one

thing is achieved:

it is inappropriate to be surprised by fine tuni

ng. Fine

tuning

is inevitable given the existence of c

omplexity

The Cosmological Constant

Not all apparent fine tunings need necessarily ari

se in the manner proposed in section 5.

At one time the extreme flatness (

) required at early epochs in order

that the

universe be

even

approximately

flat now might have been regarded as fine tuning. But its

very fineness spoke of a

mechanistic explanation, such as is provided by inflation theory.

It is possible that a mechanistic explanation may ultimately be forthcoming for the

apparent extreme tuning of the cosmological constant,

, although a

revolution in

fun

damental physics is probably required to

achieve it, Albrecht et al [5

Alternatively,

the fine tuning of

may

be an observer selection effect,

Martel et al [39], Weinberg

[53

Lineweaver

and Egan

[36

], Egan [25

The present work

offers no enlightenment on

this issue.

Relationship to the Causal Entropic Principle

The Causal Entropic Principle has been propos

ed by Bousso et al [8

10] as a criterion

for

the abundance of observers

in anthropic predictions.

These authors

define the ca

usal

entropic principle thus,

the principle asserts that physical parameters are most likely to

be found in the range of values for which the total entropy production within a causally

connected region is maximized .

They argue that,

the formation of any

complex

structure (and thus, of observers in particular), is necessarily accompanied by an

increase in the entropy of the environment. Thus, entropy production is a necessary

condition for the existence of observers. In a region where no entropy is produced, no

observers can form. The

ent

ropic principle

is the assumption that the number of

observers is proportional, on average, to the amount of

entropy produced

. Bousso et al

are

careful to emphasise that it is the matter entropy only to

which they refer

kenstein

-Hawking entropy associated with black hole or cosmological horizons

should

not be included.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

The causal entropic principle is therefore closely related to the arguments of this paper,

though not the same. We have not claimed

that entropy i

s maximised,

within any

particular region. Our assumption is weaker, namely that

reduces its entropy. This

irreversible process necessarily leads to an increase in the entropy of

. This is

consistent with the s

pirit of the causal entropic principle, but attaining a maximum has

not been assumed here.

Conclusion

Parameter sensitivity and fine tuning are two separate phenomena.

The problem of

elucidating

why the universe is parameter sensitive has not previousl

y been addressed,

despite much

effort expended on

fine tuning.

The thesis has been presented that parameter sensitivity arises as a natural consequence

of the mathematics of dynamical systems with complex outcomes. The argument is as

follows: the emergence

of complexity in a sub

system,

requires

a sequence

of entropy

reduction

s of

, which can be interpreted as a

sequence of

reducing phase space

volume

. This leads, via a very general formul

ation of system evolu

tion, to

constraint

the set of universal constants

. This is the origin of parameter sensit

ivity

Hence,

if a

universe contains

complex

parts

then parameter sensitivity is inevitably

observed

, and therefore fine t

uning will always be

required to produc

a complex world.

In other words, complex universes are generically fine tuned.

The

fine tuning

of our

universe

should therefore not elicit surprise. Moreover, any alternative universe which

gives rise to complexity, such as the model universes of Aguirre

[4],

Harnik, Kribs and

Perez [27

]

, Adams [1] or

Jaffe, Jenkins and Kimchi

[31

]

, would inevitably display

fine tuning.

This answers the question raised earlier: why could varying the universal

constants never give rise to a continuous morphing of lifefo

rms in any universe? It is

because any complex universe will be fine tuned.

This paper has

not address

ed how the universe achieves its fine tuning, only that fine

tuning is an inevitable requirement for a complex outcome.

Consequently the

extent to

which

postulating

Multiverse

may be motivated

is unchanged by the pre

sent work

Appendix

Details of

the

Toy Model for Gamow

style BBN Nucleosynthesis

The model does not bear any relationship to the physics of our universe

. It is intended

only as an illustra

tion of how fine tuning arises if a balance of chemical elements is to be

the outcome.

A nucleus of N nucleons is assumed to have a binding energy of (N

1)B, so

that any reaction between a nucleus of N nucleons and a nucleus of M nucleons to create

a nucle

us of N + M nucleons involves an increase in binding energy b

y B. All reactions

of this

form

MNMN nnn

are permitted to occur

, up to

. The rate of

these

reaction

s is set to

exp

NMC

nnnR MNMN

(A.1

)

where C =

22,000. Equ.(A.1

) gives the reaction rate in s

-1

(mole/cm

3)-1

when B is in MeV.

In our universe

the exponential

in (A.1)

would represent the Coulomb barrier which

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

would be of increasing height

for nuclei of increasing charge

. In the al

ternative universe

the

potential barrier

has been made

the same height for all nuclei.

It is important to include

a barrier term so that BBN ceases virtually completely after a

few minutes or hours. The nuclei formed during BBN are then permanent feat

ures of the

universe. But

we wish to give the heavier elements a chance of forming during BBN and

hence the barrier is made independent of atomic number. (We make no comment as to

whether this would be possible by adjusting the parameters of the standard model

quite

possibly not,

but such is not the intention).

The universal temperature

taken to be,

(A.2

)

where T is in K and t is in seconds.

The universe is

assumed to contain an equilibrium

number density of zero

mass, spin one particles (photo

ns),

given in mole/cm

by,

2436

.0 c

(A.3

)

where A = 6 x 10

-3

The total number density of nucleons is given in terms of an

assumed photon:nucleon ratio,

(A.4

)

he size sca

le of the universe varies as

in the radiation dominated era being

assumed

here, and hence the above relations are consistent with a constant number of

photons and a constant number of nucleons, though the mean energies of both are

ducing.

Since all reactions of the form

MNMN nnn

are assumed to occur, and since we

have assumed that there are no stable nuclei beyond n

, there are thus 25 contributing

reactions. The effect of these reactions on both particle creation an

d particle consumption

must be addressed. The original supply of nucleons is only consumed and not replenished

by any of these reactions (since we

not model photodisintegration directly).

Conversely, n

is only created and not consumed by any reactions

Writing t

he rate of

reaction

baba nnn

, a

n example equation

for the rate of change of the

number density of n

nuclei

is,

64636261334251

46362616332415

(A.5

)

Ten equations of this form, one for each

, comprise the complete reaction network.

These ten equations constitute the

macroscopic description of the

dynamical

system,

together with Equs.(A.1

-4

). Numerical integration by time stepping from some starting

time, t

, to some finishing time,

, is straightforward. Hence, the final abundance of each

of the nuclei is found.

The Inevitability of Fine Tuning

in a Complex Universe

, R.A.W. Bradford

Page

It is necessary, of course, to take account of universal expansion in reducing the absolute

number densities as time proceeds. This was done by multiplying all the particle

densities

by a factor

tt t at the end of each time increment, t

It remains only to define how the starting and finishing times for the integration, t

and t

are determined. The former is defined by photodisintegr

ation, and the latter by cosmic

expansion freezing

out the reactions. A full dynamical treatment would model the

photodisintegration reaction rate

MNMN nnn

. However, at high enough

temperatures there is such a numerical preponderance of phot

ons with energies in excess

of B that this photodisintegration reaction is far faster than the rate of formation of

compound nuclei. At such temperatures we can assume as a working approximation that

there are no compound nuclei present.

The

simulation

the nuclear reactions

is therefore

started

at the earliest time that the nuclei become stable against photodisintegration. By

integration of the black body spectrum, the fraction of photons with energies in excess of

B is given by,

417

.0 x

exxBE

Photons

(A.6

)

where,

11 /

and

is the highest temperature for nuclear stability. This occurs

when the fraction of photons with E > B is less than the nucleon:photon fraction, so that

is found by setting (A.6

) equal to

, i.e.,

417

.0 1

11 x

exx

(A.7

)

The time at which this occurs is then found from (A.2

) and def

ines

However, the net

rate of production of nuclear species will be virtually zero at

, since nuclear stability is

only marginal at that

time. To account for this in a very crude fashion we arbitrarily

factor the rate of nucleus formation (i.e. the forward reaction rate) by ss ttt /

for

times between

and 2

Reactions cease when their rate falls below the Hubble param

eter. Hence, the freeze

out

of the nuclear reaction

baba nnn

, whose rate is

, is assumed in our simple

treatment to occur when,

(A.8

)

Integration continues until all reactions are frozen out, which defines time

. In cases

where the freeze

-out time for the first reaction

nnn ,

is earlier than the time

which stability against photodisintegration occurs, then no nuclear reactions will take

place and there will be n

o nucleosynthesis at all.

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The Degree of Fine-Tuning in our Universe -- and Others

Preprint

Feb 2019

Fred C. Adams

(abridged) Both fundamental constants that describe the laws of physics and cosmological parameters that determine the cosmic properties must fall within a range of values in order for the universe to develop astrophysical structures and ultimately support life. This paper reviews current constraints on these quantities. The standard model of particle physics contains both coupling constants and particle masses, and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density, the vacuum energy density, the baryon-to-photon ratio, the dark matter contribution, and the amplitude of primordial density fluctuations. These quantities are constrained by the requirements that the universe lives for a long time, emerges from the BBN epoch with an acceptable chemical composition, and can successfully produce galaxies. On smaller scales, stars and planets must be able to form and function. The stars must have sufficiently long lifetimes and hot surface temperatures. The planets must be massive enough to maintain an atmosphere, small enough to remain non-degenerate, and contain enough particles to support a complex biosphere. These requirements place constraints on the gravitational constant, the fine structure constant, and composite parameters that specify nuclear reaction rates. We consider specific instances of possible fine-tuning in stars, including the triple alpha reaction that produces carbon, as well as the effects of unstable deuterium and stable diprotons. For all of these issues, viable universes exist over a range of parameter space, which is delineated herein. Finally, for universes with significantly different parameters, new types of astrophysical processes can generate energy and support habitability.

Congeniality Bounds on Quark Masses from Nucleosynthesis

Article

Dec 2012

The work of Jaffe, Jenkins and Kimchi [Phys. Rev. D79, 065014 (2009)] is revisited to see if indeed the region of congeniality found in their analysis survives further restrictions from nucleosynthesis. It is observed that much of their congenial region disappears when imposing conditions required to produce the correct and required abundances of the primordial elements as well as ensure that stars can continue to burn hydrogen nuclei to form helium as the first step in forming heavier elements in stellar nucleosynthesis. The remaining region is a very narrow slit reduced in width from around 29 MeV found by Jaffe et al. to only about 2.2 MeV in the difference of the nucleon/quark masses. Further bounds on

\delta m_q /m_q

seem to reduce even this narrow slit to the physical point itself.

The Challenge of Chance: A Multidisciplinary Approach from Science and the Humanities

Book

Full-text available

Jan 2016

This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts. A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.

The Fine-Tuning Argument: Exploring the Improbability of Our Existence

Chapter

Full-text available

May 2016

Klaas Landsman

Our laws of nature and our cosmos appear to be delicately fine-tuned for life to emerge, in a way that seems hard to attribute to chance. In view of this, some have taken the opportunity to revive the scholastic Argument from Design, whereas others have felt the need to explain this apparent fine-tuning of the clockwork of the Universe by proposing the existence of a ‘Multiverse’. We analyze this issue from a sober perspective. Having reviewed the literature and having added several observations of our own, we conclude that cosmic fine-tuning supports neither Design nor a Multiverse, since both of these fail at an explanatory level as well as in the more quantitative context of Bayesian confirmation theory (although there might be other reasons to believe in these ideas, to be found in religion and in inflation and/or string theory, respectively). In fact, fine-tuning and Design even seem to be at odds with each other, whereas the inference from fine-tuning to a Multiverse only works if the latter is underwritten by an additional metaphysical hypothesis we consider unwarranted. Instead, we suggest that fine-tuning requires no special explanation at all, since it is not the Universe that is fine-tuned for life, but life that has been fine-tuned to the Universe.

The degree of fine-tuning in our universe–and others

Article

Feb 2019
PHYS REP

Fred C. Adams

Both the fundamental constants that describe the laws of physics and the cosmological parameters that determine the properties of our universe must fall within a range of values in order for the cosmos to develop astrophysical structures and ultimately support life. This paper reviews the current constraints on these quantities. The discussion starts with an assessment of the parameters that are allowed to vary. The standard model of particle physics contains both coupling constants (α,α s ,α w ) and particle masses (m u ,m d ,m e ), and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density of the universe (Ω), the contribution from vacuum energy (ρ Λ ), the baryon-to-photon ratio (η), the dark matter contribution (δ), and the amplitude of primordial density fluctuations (Q). These quantities are constrained by the requirements that the universe lives for a sufficiently long time, emerges from the epoch of Big Bang Nucleosynthesis with an acceptable chemical composition, and can successfully produce large scale structures such as galaxies. On smaller scales, stars and planets must be able to form and function. The stars must be sufficiently long-lived, have high enough surface temperatures, and have smaller masses than their host galaxies. The planets must be massive enough to hold onto an atmosphere, yet small enough to remain non-degenerate, and contain enough particles to support a biosphere of sufficient complexity. These requirements place constraints on the gravitational structure constant (α G ), the fine structure constant (α), and composite parameters (C ⋆ ) that specify nuclear reaction rates. We then consider specific instances of possible fine-tuning in stellar nucleosynthesis, including the triple alpha reaction that produces carbon, the case of unstable deuterium, and the possibility of stable diprotons. For all of the issues outlined above, viable universes exist over a range of parameter space, which is delineated herein. Finally, for universes with significantly different parameters, new types of astrophysical processes can generate energy and thereby support habitability.

The Beginning and the End: The Meaning of Life in a Cosmological Perspective

Book

Full-text available

Jun 2014

Clément Vidal

In this fascinating journey to the edge of science, Vidal takes on big philosophical questions: Does our universe have a beginning and an end or is it cyclic? Are we alone in the universe? What is the role of intelligent life, if any, in cosmic evolution? Grounded in science and committed to philosophical rigor, this book presents an evolutionary worldview where the rise of intelligent life is not an accident, but may well be the key to unlocking the universe's deepest mysteries. Vidal shows how the fine-tuning controversy can be advanced with computer simulations. He also explores whether natural or artificial selection could hold on a cosmic scale. In perhaps his boldest hypothesis, he argues that signs of advanced extraterrestrial civilizations are already present in our astrophysical data. His conclusions invite us to see the meaning of life, evolution and intelligence from a novel cosmological framework that should stir debate for years to come.

The Fine-Tuning Argument

Article

May 2015

Klaas Landsman

Our laws of nature and our cosmos appear to be delicately fine-tuned for life to emerge, in way that seems hard to attribute to chance. In view of this, some have taken the opportunity to revive the scholastic Argument from Design, whereas others have felt the need to explain this apparent fine-tuning of the clockwork of the Universe by proposing the existence of a `Multiverse'. We analyze this issue from a sober perspective. Having reviewed the literature and having added several observations of our own, we conclude that cosmic fine-tuning supports neither Design nor a Multiverse, since both of these fail at an explanatory level as well as in a more quantitative context of Bayesian confirmation theory (although there might be other reasons to believe in these ideas, to be found in religion and in inflation and/or string theory, respectively). In fact, fine-tuning and Design even seem to be at odds with each other, whereas the inference from fine-tuning to a Multiverse only works if the latter is underwritten by an additional metaphysical hypothesis we consider unwarranted. Instead, we suggest that fine-tuning requires no special explanation at all, since it is not the Universe that is fine-tuned for life, but life that has been fine-tuned to the Universe.

Irreducibility and Computational Equivalence: 10 Years After Wolfram's A New Kind of Science

Book

Jan 2013

Hector Zenil

We explore several concepts for analyzing the intuitive notion of computational irreducibility and we propose a robust formal definition, first in the field of cellular automata and then in the general field of any computable function f from N to N. We prove that, through a robust definition of what means "to be unable to compute the nth step without having to follow the same path than simulating the automaton or the function", this implies genuinely, as intuitively expected, that if the behavior of an object is computationally irreducible, no computation of its nth state can be faster than the simulation itself.

Life at the Interface of Particle Physics and String Theory

Article

Full-text available

Jun 2013

A.N. Schellekens

If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all non-gravitational physics: the Standard Model. But despite this monumental achievement there is a clear sense of disappointment: many questions remain unanswered. Remarkably, most unanswered questions could just be environmental, and disturbingly (to some) the existence of life may depend on that environment. Meanwhile there has been increasing evidence that the seemingly ideal candidate for answering these questions, String Theory, gives an answer few people initially expected: a huge "landscape" of possibilities, that can be realized in a multiverse and populated by eternal inflation. At the interface of "bottom-up" and "top-down" physics, a discussion of anthropic arguments becomes unavoidable. We review developments in this area, focusing especially on the last decade.

The Beginning and the End: The Meaning of Life in a Cosmological Perspective

Book

Jan 2013

Clement Vidal

Where does it all come from? Where are we going? Are we alone in the universe? What is good and what is evil? The scientific narrative of cosmic evolution demands that we tackle such big questions with a cosmological perspective. I tackle the first question in Chapters 4-6; the second in Chapters 7-8; the third in Chapter 9 and the fourth in Chapter 10. However, where do we start to answer such questions? In Chapters 1-3, I elaborate the concept of worldview and argue that we should aim at constructing comprehensive and coherent worldviews. In Chapter 4, I identify seven fundamental challenges to any ultimate explanation. I conclude that our explanations tend to fall in two cognitive attractors, the point or the cycle. In Chapter 5, I focus on the free parameters issue, while Chapter 6 is a critical analysis of the fine-tuning issue. I conclude that fine-tuning is a conjecture and that we need to further study how typical our universe is. This opens a research endeavor that I call artificial cosmogenesis. In Chapter 7, I show the importance of artificial cosmogenesis from extrapolating the future of scientific simulations. I then analyze two other evolutionary explanations of fine-tuning in Chapter 8: Cosmological Natural Selection and the broader scenario of Cosmological Artificial Selection. In Chapter 9, I inquire into the search for extraterrestrials and conclude that some binary star systems are good candidates. Since those putative beings feed on stars, I call them starivores. The question of their artificiality remains open, but I propose a prize to further continue and motivate the scientific assessment of this hypothesis. In Chapter 10, I explore foundations to build a cosmological ethics and conclude that the ultimate good is the infinite continuation of the evolutionary process. Appendix I summarizes my position and Appendix II provides argumentative maps of the entire thesis.

The Origins of Order: Self-Organization and Selection in Evolution

Book

Jun 1993

Stuart A Kauffman

Stuart Kauffman here presents a brilliant new paradigm for evolutionary biology, one that extends the basic concepts of Darwinian evolution to accommodate recent findings and perspectives from the fields of biology, physics, chemistry and mathematics. The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of self-organization: the spontaneous emergence of order widely observed throughout nature. Kauffman here argues that self-organization plays an important role in the emergence of life itself and may play as fundamental a role in shaping life's subsequent evolution as does the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt remain poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems, contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biological science itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences.

Probabilities and the fine-tuning argument: A sceptical view

Article

Jan 2001

Proponents of the FineTuning Argument frequently assume that the narrowness of the lifefriendly range of fundamental physical constants implies a low probability for the origin of the universe 'by chance'. We cast this argument in a more rigorous form than is customary and conclude that the narrow intervals do not yield a probability at all because the resulting measure function is nonnormalizable. We then consider various attempts to circumvent this problem and argue that they fail.

The Anthropic Principle and the Mass Scale of the Standard Model

Article

Jul 1997

Why is the CMB fluctuation level 10^{-5}?

Article

Sep 1997

Multiverse cosmological models

Article

Nov 2011
MOD PHYS LETT A

Paul C W Davies

Recent advances in string theory and inflationary cosmology have led to a surge of interest in the possible existence of an ensemble of cosmic regions, or "universes", among the members of which key physical parameters, such as the masses of elementary particles and the coupling constants, might assume different values. The observed values in our cosmic region are then attributed to an observer selection effect (the so-called anthropic principle). The assemblage of universes has been dubbed "the multiverse". In this paper we review the multiverse concept and the criticisms that have been advanced against it on both scientific and philosophical grounds.

The World as a Hologram

Article

Jan 1995

L. Susskind

According to 't Hooft the combination of quantum mechanics and gravity requires the three-dimensional world to be an image of data that can be stored on a two-dimensional projection much like a holographic image. The two-dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three-dimensional phenomena. After outlining 't Hooft's proposal we give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high-energy particle collisions are described. The phenomenon of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound from causality. Finally we consider string theory as a possible realization of 't Hooft's idea. The light front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic theory are demonstrated. The agreement between the two requires unproven but plausible assumptions about the nonperturbative behavior of string theory. Very similar ideas to those in this paper have long been held by Charles Thorn.

The Origins of Order

Book

Jan 1993

Stuart A. Kauffman

The Accidental Universe

Article

Jan 1983

P. C. W. Davies

Energy in the Universe

Article

Sep 1971

Freeman J. Dyson

Energy flows in the universe are described and the genesis of the various kinds of energy is discussed. The process by which energy is channeled in the cosmos are discussed with implications for the earth highlighted.

Report of the Dark Energy Task Force

Article

Apr 2006

Andreas Albrecht

Understanding the observed cosmic acceleration is widely ranked among the very most compelling of all outstanding problems in physical science. Many believe that nothing short of a revolution will be required in order to integrate the cosmic acceleration (often attributed to ``dark energy'') with our understanding of fundamental physics. The DETF was formed at the request of DOE, NASA and NSF as a joint subcommittee of the Astronomy and Astrophysics Advisory Committee (AAAC) and the High Energy Physics Advisory Panel (HEPAP) to give advice on optimizing our program of dark energy studies. To this end we have assessed a wide variety of possible techniques and strategies. I will present our main conclusions and discuss their implications.

The Inevitability of Fine Tuning in a Complex Universe

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