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The anthropic principle: science, philosophy or guesswork?


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Slides elaborated to illustrate the intervention of Mariano Artigas in the Summer School, June 10-15 2004: "The Impact of the Humanities on the Development of European Science", Venice (Italy). Organized by the Istituto Veneto di Scienze, Lettere ed Arti and the Galileo Chair of History of Science of the University of Padua.

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The anthropic principle: science, philosophy or guesswork?

  1. 1. THE ANTHROPIC PRINCIPLE: SCIENCE, PHILOSOPHY OR GUESSWORK ? Mariano Artigas Department of Philosophy University of Navarra Pamplona (Spain) The Impact of the Humanities on the Development of European Science SUMMER SCHOOL 10-15 JUNE 2004 Venice (Italy)
  2. 2. Ernan McMullin (1981) Basic science, at its most innovative, merges into philosophy
  3. 3. Robert Dicke (1961) It is well known that carbon is required to make physicists
  4. 4. Nick Bostrom (2002) A total of over thirty anthropic principles have been formulated and many of them have been defined several times over – in nonequivalent ways – by different authors, and sometimes even by the same authors on different occasions. Not surprisingly, the result has been some pretty wild confusion concerning what the whole thing is about.
  6. 6. 1 CONSTANTS OF NATURE AND NATURAL UNITS 1.1. The Constants of Nature 1.2. Natural Units: George Stoney (1874) 1.3. Natural Units: Max Planck (1899)
  7. 7. 1.1. The Constants of Nature Charge of an electron (e) = 1.602 x 10-19 coulombs Speed of light in a vacuum (c)= 2.99792458 x 108 m s-1 (roughly 300,000 kilometers per second) Planck constant (h) = 6.626 176 x 10-34 Js ħ = h / 2π = 1.054589 x 10-34 Js Gravitational constant (G) = 6.67259 x 10-11 N m2 kg-2 (m3 kg-1 s-2 ) Fine structure constant (α) α = e2 / 2ε0 hc ≅ 1 /137 Other universal constants are known (some 19 in total): the Boltzmann constant, the mass of an electron, the mass of a proton, Avogadro’s number, the gas constant, the Rydberg constant, and so on.
  8. 8. John Barrow on the constants of nature This is the Holy Grail of fundamental physics and it means the numerical calculation of one of the constants of Nature. This has never been done. So far, the only way we can know their values is by measuring them. This seems unsatisfactory. It allows the constants that appear in our theories to have a huge range of different possible values without overthrowing the theory (2002)
  9. 9. 1.2. Natural Units: George Stoney (1874) (1) George Johnstone Stoney 1826-1911
  10. 10. 1.2. Natural Units: George Stoney (1874) (2) M = (e2 / G)1/2 = 10-7 gram L = (Ge2 / c4 )1/2 = 10-37 metres T = (Ge2 / c6 )1/2 = 3 x10-46 seconds 45 minutes = 9 x10-44 Stoney-time!
  11. 11. 1.3. Natural Units: Max Planck (1899-1900) (1) m = (hc / G)1/2 = 5,56 x 10-5 gram l = (Gh / c3 )1/2 = 4,13 x 10-33 cm t = (Gh / c5 )1/2 = 1,38 x10-43 sec T = k-1 (hc5 / G)1/2 = 3,5 x1032 K
  12. 12. 1.3. Natural Units: Max Planck (1899-1900) (2) Planck’s units mark the boundary of applicability of our current theories. The constants of Nature mark out the frontiers of our existing knowledge and show us where our theories start to overreach themselves (John Barrow)
  13. 13. 2 THE DIMENSIONLESS CONSTANTS OF NATURE 2.1. Einstein’s Search for the Ultimate Theory of Physics 2.2. Dimensionless Constants and Other Worlds
  14. 14. 2.1. Einstein’s Search for the Ultimate Theory of Physics (1) God does not play dice
  15. 15. Albert Einstein (1945) (2) There are two kinds of constants: apparent and real ones. The apparent ones are simply the outcome of the introduction of arbitrary units, but are eliminable. The real [true] ones are genuine numbers which God had to choose arbitrarily, as it were, when He deigned to create this world.
  16. 16. Albert Einstein (1945) (3) Or one could put it like this: In a reasonable theory there are no dimensionless numbers whose values are only empirically determinable. Of course, I cannot prove this. But I cannot imagine a unified and reasonable theory which explicitly contains a number which the whim of the Creator might just as well have chosen differently, whereby a qualitatively different lawfulness of the world would have resulted. Or one could put it like this: A theory which in its fundamental equations explicitly contains a non- basic constant would have to be somehow constructed from bits and pieces which are logically independent of each other; but I am confident that this world is not such that so ugly a construction is needed for its theoretical comprehension.
  17. 17. 2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (1) The identification of dimensionless constants of Nature like α and αG , along with the numbers that play the same defining role for the weak and strong forces of Nature encourages us to think for a moment about worlds others than our own. These other worlds may be defined by laws of Nature which are the same as those which govern the Universe as we know it but they will be characterised by different values of dimensionless constants. These numerical shifts will alter the whole fabric of our imaginary worlds. The balances between their forces will be different from those in our world. Atoms may have different properties. Gravity may play a role in the small- scale world. The quantum nature of reality may enter in unexpected places. α = 2π e2 / hc ≈ 1 / 137 αG= Gmpr 2 /hc ≈ 10-38
  18. 18. 2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (2) The last important lesson we learn from the way that pure numbers like α define the world is what it really means for world to be different. The pure number that we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck’s constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h and e were changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world could be observationally indistinguishable from our world. The only thing that counts in the definition of the world are the vales of the dimensionless constants of Nature. If all masses are doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged
  19. 19. 3 DIMENSIONLESS CONSTANTS AND LARGE NUMBERS 3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (1935) 3.2. Large Number’s Coincidences Are Not Accidental: Paul Dirac (1937)
  20. 20. 3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (1) Four pure dimensionless numbers (the ultimate constants) Ratio of the masses of the proton and electron: mpr / me ≈ 1840 The inverse of the fine structure constant: 2πh / e2 ≈ 137 Ratio of the gravitational force to the electromagnetic force between and electron and a proton: e2 / Gmprme ≈ 1040 Number of protons in the visible universe: NEdd ≈ 1080 (1882-1944)
  21. 21. 3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (2) Are these four constants irreducible, or will a further unification of physics show that some or all of them can be dispensed with? Could they have been different from what they actually are?... the question arises whether the above ratios can be assigned arbitrarily or whether they are inevitable. In the former case we can only learn their values by measurement; in the latter case it is possible to find them by theory... I think the opinion now widely prevails that the [above four] constants... are not arbitrary but will ultimately be found to have a theoretical explanation; though I have also hears the contrary view expressed.
  22. 22. Dimensionless numbers with an “strange” appearance: related with 1040 , its squares and cubes Total number of protons in the observable universe: 1080 Ratio of the strengths of electromagnetic and gravitational forces between two protons: 1040 “Action” of the observable universe in units of the fundamental Planck units of action: 10120 Cosmological constant in units of the square of the Planck length: 10-120
  23. 23. John D. Barrow on Eddington Eddington had tried to build a theory that made their [large numbers] appearance understandable. But he failed to convince a significant body of cosmologists that he was on the right track. Yet Eddington succeeded in persuading people that there was something that needed explaining. Completely unexpectedly, it was one of his famous neighbours in Cambridge who wrote the short letter to the journal Nature which succeeded in fanning interest in the problem with an idea that remains a viable possibility even to this day [Paul Dirac].
  24. 24. 3.2. Large Number’s Coincidences Are Not Accidental: Paul Dirac (1937)(1) (1902-1984) Now, you might say, this is a remarkable coincidence. But it is rather hard to believe that. One feels that there must be some connection between these very large numbers, a connection which we cannot explain at present but which we shall be able to explain in the future when we have a better knowledge both of atomic theory and of cosmology. Let us assume that these two numbers are connected. Now one of these numbers is not a constant. The age of the universe, of course, gets bigger and bigger as the universe gets older. So the other one must be increasing also in the same proportion. Large Numbers Hypothesis
  25. 25. Paul Dirac (2) Any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity.
  26. 26. 4 THE FORMULATION OF THE ANTHROPIC PRINCIPLE 4.1. Introducing Anthropic Reasoning: Gerald Whitrow (1955) 4.2. More Anthropic Reasoning: Robert Dicke (1961) 4.3. The principle is Almost There: Collins and Hawking (1973) 4.4. The Birth of the Anthropic Principle: Brandon Carter (1973)
  27. 27. 4.1. Introducing Anthropic Reasoning: Gerald Whitrow (1955) I suggest that a possible clue to the elucidation of this problem is provided by the fact that physical conditions on the Earth have been such that the evolution of Man has been possible. A new attempt to throw light on the question indicates that this fundamental topological property of the world may possibly be regarded as partly contingent and partly necessary, since it could be inferred as the unique natural concomitant of certain other contingent characteristics associated with the evolution of the higher forms of terrestrial life, in particular of Man, the formulator of the problem. 1902-2000
  28. 28. 4.2. More Anthropic Reasoning: Robert Dicke (1961) with the assumption of an evolutionary universe, T [the Hubble age of the universe] is not permitted to take one of an enormous range of values, but is somewhat limited by the biological requirements to be met during the epoch of man. Thus, contrary to our original supposition, T is not a “random choice” from a wide range of possible choices, but is limited by the criteria for the existence of physicists.
  29. 29. 4.3. The principle is Almost There: Collins and Hawking (1973)
  30. 30. 4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (1) ANTHROPIC PRINCIPLE what we can expect to observe must be restricted by the conditions necessary for our presence as observers. (Although our situation is not necessarily central, it is inevitably privileged to some extent).
  31. 31. 4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (2) WEAK ANTHROPIC PRINCIPLE We must be prepared to take account of the fact that our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers
  32. 32. 4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (3) STRONG ANTHROPIC PRINCIPLE The Universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage. To paraphrase Descartes, “Cogito ergo mundus talis est”
  33. 33. Carter on Anthropic Principle, 1973 (1) It is of course always philosophically possible – as a last resort, when no stronger physical argument is available - to promote a prediction based on the strong anthropic principle to the status of an explanation by thinking in terms of a “world ensemble”... The existence of any organism describable as an observer will only be possible for certain restricted combinations of the parameters, which distinguish within the world-ensemble an exceptional cognizable subset.
  34. 34. Carter on Anthropic Principle, 1973 (2) The acceptability of predictions of this kind as explanations depends on one’s attitude to the world ensemble concept. Although the idea that there may exist many universes, of which only one can be known to us, may at first sight seem philosophically undesirable, it does not really go very much further than the Everett doctrine to which one is virtually forced by the internal logic of quantum theory.
  35. 35. 5 THE ANTHROPIC PRINCIPLE COMES OF AGE 5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) 5.2. A Meeting of the Royal Society (1983) 5.3. Carter Revisited by Carter (1983) 5.4. John D. Barrow and Frank J. Tipler on the Anthropic Principle (1986)
  36. 36. 5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (1) Sir Martin Rees Several aspects of our Universe – some of which seem to be prerequisites for the evolution of any form of life – depend rather delicately on apparent ‘coincidences’ among the physical constants
  37. 37. 5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (2) Sir Martin Rees The possibility of life as we know it evolving in the Universe depends on the values of a few basic physical constants – and is in some respects remarkably sensitive to their numerical values
  38. 38. 5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (3) Sir Martin Rees One day, we may have a more physical explanation for some of the relationships discussed here that now seem genuine coincidences... However, even if all apparently anthropic coincidences could be explained in this way, it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life.
  39. 39. 5.2. A Meeting of the Royal Society (1983) interest in [anthropic principle] in recent times originally instigated the proposal to hold this Discussion. However, because of their speculative character and of their inability as yet to produce new predictions, it was considered that the main emphasis ought to be upon the study of the constants themselves rather than the role of the constants in these applications.
  40. 40. 5.3. Carter Revisited by Carter (1983) (1) The practical scientific utility of this principle arises from its almost tautological corollary to the effect that in making general inferences from what we observe in the Universe, we must allow for the fact that our observations are inevitably biased by selection effects arising from the restriction that our situation should satisfy the conditions that are necessary a priori, for our existence. The term self- selection principle would be an alternative and perhaps more appropriate description for this hardly questionable but easily overlooked precept.
  41. 41. 5.3. Carter Revisited by Carter (1983) (2) If I had guessed that the term ‘anthropic principle’ would come to be so widely adopted I would have been more careful in my original choice of words. The imperfection of this now standard terminology is that it conveys the suggestion that the principle applies only to mankind. However, although this is indeed the case as far as we can apply it ourselves, it remains true that the same self-selection principle would be applicable by any extraterrestrial civilization that may exist.
  42. 42. 5.3. Carter Revisited by Carter (1983) (3) As I originally formulated it (Carter 1974) this ‘strong’ principle consisted in the remark that our mere existence as intelligent observers imposes restrictions not just on our situation but even on the general properties of the Universe, including the values of the fundamental parameters that are the subject of the present meeting. Although this ‘principle’ has aroused considerable enthusiasm in certain quarters, it is not something that I would be prepared to defend with the same degree of conviction as is deserved by its ‘weak’ analogue.
  43. 43. 5.4. Barrow and Tipler on the Anthropic Principle (1986) (1) WEAK ANTHROPIC PRINCIPLE The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon- based life can evolve and by the requirement that the Universe be old enough for it to have already done so. Much stronger than Carter’s weak principle
  44. 44. 5.4. Barrow and Tipler on the Anthropic Principle (1986) (2) STRONG ANTHROPIC PRINCIPLE The Universe must have those properties which allow life to develop within it at some stage in its history. If we speak of this universe where we are, yes, of course If we speak of universes in general, why?
  45. 45. Confusion increases: an example Later, Carter also proposed the Strong Anthropic Principle (SAP), which states that the Universe had to bring humanity into being. This version is much more teleological, if not theological, and is of a highly speculative nature. Nonetheless, Carter had scientific reasons to propose it.
  46. 46. 6 FINE-TUNING, TELEOLOGY, AND OTHER WORLDS 6.1. Fine-Tuning 6.2. The Teleological Argument 6.3. Many Worlds 6.4. Observation Selection Effects
  47. 47. 6.1. Fine-Tuning One aspect of anthropic reasoning that has attracted plenty of attention, from both philosophers and physicists, is its use in cosmology to explain the apparent fine-tuning of our universe. “Fine-tuning” refers to the supposed fact that there is a set of cosmological parameters or fundamental physical constants that are such that had they been very slightly different, the universe would have been void of intelligent life. (Nick Bostrom) EXAMPLES - rate of expansion of the universe - relations between fundamental masses and forces - topological and metrical properties of space-time
  48. 48. 6.2. The Teleological Argument (1) The fifth way is taken from things’ being directed. We see that there are things that have no knowledge, like physical bodies, but which act for the sake of an end. This is clear in that they always, or for the most part, act in the same way, and achieve what is best. This shows that they reach their end not by chance but in virtue of some tendency. But things which have no knowledge do not have a tendency to an end unless they are directed by something that does have knowledge and understanding. An example is an arrow directed by an archer. Therefore there is some being with understanding which directs all things to their end, and this, we say, is God. Thomas Aquinas
  49. 49. It is impossible for things contrary and discordant to fall into one harmonious order always or for the most part, except under some one guidance, assigning to each and all a tendency to a fixed end. But in the world we see things of different natures falling into harmonious order, not rarely and fortuitously, but always or for the most part. Therefore there must be some Power by whose providence the world is governed; and that we call God 6.2. The Teleological Argument (2) Thomas Aquinas
  50. 50. 6.3. Many Worlds (1) Some philosophers and physicists take fine-tuning to be an explanandum that cries out for an explanans. Two possible explanations are usually envisioned: the design hypothesis and the ensemble hypothesis. Although these explanations are compatible, they tend to be viewed as competing. If we knew that one of them were correct, there would be less reason to accept the other. Nick Bostrom
  51. 51. 6.3. Many Worlds (2) In contrast to some versions of the design hypothesis, the meaningfulness of the ensemble hypothesis is not much in question. Only those subscribing to a very strict verificationist theory of meaning would deny that it is possible that the world might contain a large set of causally fairly disconnected spacetime regions with varying physical parameters. Nick Bostrom
  52. 52. 6.3. Many Worlds (3) Cosmologists have suggested numerous ways in which greatly many, greatly varied universes could be generated... In short, modern theorists find it easy to invent mechanisms for making apparent physics and overt properties differ from one universe to another even when the underlying physics and the most fundamental properties remain always the same. John Leslie
  53. 53. 6.3. Many Worlds (4) In my model, I assume that our Universe did indeed appear from nowhere about 1010 yr ago. Contrary to widespread belief, such an event need not have violated any of the conventional laws of physics. The laws of physics merely imply that a Universe which appears from nowhere must have certain specific properties. In particular, such a Universe must have a zero net value for all conserved quantities... I offer the modest proposal that our universe is simply one of those things which happen from time to time. E. P. Tryon, “: Nature, 246 (1973), No. 5433, pp. 396-397
  54. 54. 6.3. Many Worlds (5) Max Tegmark
  55. 55. Max Tegmark (Scientific American, May 2003) Not just a staple of science fiction, other universes are a direct implication of cosmological observations. Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on... ... In infinite space, even the most unlikely events must take place somewhere. There are infinitely many other inhabited planets, including not just one but infinitely many that have people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.
  56. 56. Max Tegmark (Scientific American, May 2003) The Reality Postulate One of the many implications of recent cosmological observations is that the concept of parallel universes is no mere metaphor. Spare appears to be infinite in size. If so, then somewhere out there, everything that is possible becomes real, no matter how improbable it is... ... And this is fairly solid physics.
  57. 57. Alan Guth the inflationary universe
  58. 58. The inflationary universe One of the intriguing consequences of inflation is that quantum fluctuations in the early universe can be stretched to astronomical proportions, providing the seeds for the large scale structure of the universe. The predicted spectrum of these fluctuations was calculated by Guth and others in 1982. These fluctuations can be seen today as ripples in the cosmic background radiation, but the amplitude of these faint ripples is only about one part in 100,000. Nonetheless, these ripples were detected by the COBE satellite in 1992, and they have now been measured to much higher precision by the WMAP satellite and other experiments. The properties of the radiation are found to be in excellent agreement with the predictions of the simplest models of inflation.
  59. 59. Andrei Linde eternal chaotic inflation?
  60. 60. Eternal chaotic inflation Initially, inflation was considered as an intermediate stage of the evolution of the universe, which was necessary to solve many cosmological problems... inflation was a part of the big bang theory. Gradually, however, the big bang theory became a part of inflationary cosmology. Recent versions of inflationary theory assert that instead of being a single, expanding ball of fire described by the big bang theory, the universe looks like a huge growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more new balls, ad infinitum. Therefore the evolution of the universe has no end and may have no beginning.
  61. 61. 6.4. Observation Selection Effects Another example, taken from Sir Arthur Eddington: suppose you are trying to catch fish with a net that doesn’t catch fish that are shorter than 20 cm. If you use such a net to catch a hundred fish and they all turn out to be 20 cm or longer, then obviously you are not allowed to regard this as evidence that the minimum length of fish in the lake is 20 cm. Nick Bostrom Anthropical reasoning is a kind of observation selection effect
  63. 63. In the end... perhaps the most significant change in cosmological thinking involves a new willingness to discuss what used to be an idea that was not normally mentioned in polite company: the anthropic principle... The realization that an extremely small, but non-zero, cosmological constant might exist has changed physicists’ interest in anthropic explanation of nature precisely because the value it seems to take is otherwise so inexplicable... In the end as with so many anthropic arguments, it is hard to know what to make of this result, especially in the absence of any fundamental theory. Lawrence M. Krauss, “A just-so story”, Nature, vol. 423 (15 May 2003), pp. 230-231.