Infinity

George F. R. Ellis weighs in on the concept of infinity in his excellent paper, Issues in the Philosophy of Cosmology, available on astro-ph at https://arxiv.org/abs/astro-ph/0602280. He writes:

9.3.2 Existence of Infinities

The nature of existence is significantly different if there is a finite amount of matter or objects in the universe, as opposed to there being an infinite quantity in existence. Some proposals claim there may be an infinite number of universes in a multiverse and many cosmological models have spatial sections that are infinite, implying an infinite number of particles, stars, and galaxies. However, infinity is quite different from a very large number! Following David Hilbert, one can suggest these unverifiable proposals cannot be true: the word “infinity” denotes a quantity or number that can never be attained, and so will never occur in physical reality.38 He states:

Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea . . . which transcends all experience and which completes the concrete as a totality . . .

This suggests “infinity” cannot be arrived at, or realized, in a concrete physical setting; on the contrary, the concept itself implies its inability to be realized!

Thesis I2: The often claimed physical existence of infinities is questionable. The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.

This applies in principle to both small and large scales in any single universe:

The existence of a physically existing spacetime continuum represented by a real (number) manifold at the micro-level contrasts with quantum gravity claims of a discrete spacetime structure at the Planck scale, which one might suppose was a generic aspect of fully non-linear quantum gravity theories. In terms of physical reality, this promises to get rid of the uncountable infinities the real line continuum engenders in all physical variables and fields40. There is no experiment that can prove there is a physical continuum in time or space; all we can do is test space-time structure on smaller and smaller scales, but we cannot approach the Planck scale.

Infinitely large space-sections at the macro-level raise problems as indicated by Hilbert, and leads to the infinite duplication of life and all events. We may assume space extends forever in Euclidean geometry and in many cosmological models, but we can never prove that any realised 3-space in the real universe continues in this way—it is an untestable concept, and the real spatial geometry of the universe is almost certainly not Euclidean. Thus Euclidean space is an abstraction that is probably not physically real. The infinities supposed in chaotic inflationary models derive from the presumption of pre-existing infinite Euclidean space sections, and there is no reason why those should necessarily exist. In the physical universe spatial infinities can be avoided by compact spatial sections, resulting either from positive spatial curvature, or from a choice of compact topologies in universes that have zero or negative spatial curvature. Machian considerations to do with the boundary conditions for physics suggest this is highly preferable; and if one invokes string theory as a fundamental basis for physics, the “dimensional democracy” suggests the three large spatial dimensions should also be compact, since the small (“compactified”) dimensions are all taken to be so. The best current data from CBR and other observations indeed suggest k = +1, implying closed space sections for the best-fit FL model.

The existence of an eternal universe implies that an infinite time actually exists, which has its own problems: if an event happens at any time t0, one needs an explanation as to why it did not occur before that time (as there was an infinite previous time available for it to occur); and Poincaré eternal return will be possible if the universe is truly cyclic. In any case it is not possible to prove that the universe as a whole, or even the part of the universe in which we live, is past infinite; observations cannot do so, and the physics required to guarantee this would happen (if initial conditions were right) is untestable. Even attempting to prove it is future infinite is problematic (we cannot for example guarantee the properties of the vacuum into the infinite future—it might decay into a state corresponding to a negative effective cosmological constant).

It applies to the possible nature of a multiverse. Specifying the geometry of a generic universe requires an infinite amount of information because the quantities necessary to do so are fields on spacetime, in general requiring specification at each point (or equivalently, an infinite number of Fourier coefficients): they will almost always not be algorithmically compressible. All possible values of all these components in all possible combinations will have to occur in a multiverse in which “all that can happen, does happen”. There are also an infinite number of topological possibilities. This greatly aggravates all the problems regarding infinity and the ensemble. Only in highly symmetric cases, like the FL solutions, does this data reduce to a finite number of parameters, each of which would have to occur in all possible values (which themselves are usually taken to span an infinite set, namely the entire real line). Many universes in the ensemble may themselves have infinite spatial extent and contain an infinite amount of matter, with all the problems that entails. To conceive of physical creation of an infinite set of universes (most requiring an infinite amount of information for their prescription, and many of which will themselves be spatially infinite) is at least an order of magnitude more difficult than specifying an existent infinitude of finitely specifiable objects.

One should note here particularly that problems arise in the multiverse context from the continuum of values assigned by classical theories to physical quantities. Suppose for example that we identify corresponding times in the models in an ensemble and then assume that all values of the density parameter and the cosmological constant occur at each spatial point at that time. Because these values lie in the real number continuum, this is a doubly uncountably infinite set of models. Assuming genuine physical existence of such an uncountable infinitude of universes is the antithesis of Occam’s razor. But on the other hand, if the set of realised models is either finite or countably infinite, then almost all possible models are not realised. And in any case this assumption is absurdly unprovable. We can’t observationally demonstrate a single other universe exists, let alone an infinitude. The concept of infinity is used with gay abandon in some multiverse discussions, without any concern either for the philosophical problems associated with this statement, or for its completely unverifiable character. It is an extravagant claim that should be treated with extreme caution.

38An intriguing further issue is the dual question: Does the quantity zero occur in physical reality? This is related to the idea of physical existence of nothingness, as contrasted with a vacuum. A vacuum is not nothing!

40To avoid infinities entirely would require that nothing whatever is a continuum in physical reality (since any continuum interval contains an infinite number of points). Doing without that, conceptually, would mean a complete rewrite of many things. Considering how to do so in a way compatible with observation is in my view a worthwhile project.


So, given this discussion of infinities, the answer to the doubly hypothetical question, “Can God make a rock so big he can’t pick it up?” is likely a “Yes”! – D.O.

Multiverse

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.2 Issue H: The possible existence of multiverses
If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist; and this can help explain the fine-tuned nature of many parameters whose values are otherwise unconstrained by physics.  As discussed in the previous section, there are a number of ways in which, theoretically, multiverses could be realized.  They provide a way of applying probability to the universe (because they deny the uniqueness of the universe).  However, there are a number of problems with this concept.  Besides, this proposal is observationally and experimentally untestable; thus its scientific status is debatable.

My 100-year-old uncle—a lifelong teacher and voracious reader who is still intellectually active—recently sent me Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, published by Vintage Books in 2014. I could not have had a more engaging introduction to the concept of the Multiverse. Tegmark presents four levels of multiverses that might exist. They are

Level I Multiverse: Distant regions of space with the same laws of physics that are currently but not necessarily forever unobservable.

Level II Multiverse: Distant regions of space that may have different laws of physics and are forever unobservable.

Level III Multiverse: Quantum events at any location in space and in time cause reality to split and diverge along parallel storylines.

Level IV Multiverse: Space, time, and the Level I, II, and III multiverses all exist within mathematical structures that describe all physical existence at the most fundamental level.

There seems little question that our universe is very much larger than the part that we can observe. The vast majority of our universe is so far away that light has not yet had time to reach us from those regions. Whether we choose to call the totality of these regions the universe or a Level I multiverse is a matter of semantics.

Is our universe or the Level I multiverse infinite? Most likely not. That infinity is a useful mathematical construct is indisputable. That infinite space or infinite time exists is doubtful. Both Ellis and Tegmark agree on this and present cogent arguments as to why infinity cannot be associated with physical reality. Very, very large, or very, very small, yes, but not infinitely large or infinitely small.

Does a Level II, III, and IV multiverse exist? Tegmark thinks so, but Ellis raises several objections, noted above and elsewhere. The multiverse idea remains quite controversial, but as Tegmark writes,

Even those of my colleagues who dislike the multiverse idea now tend to grudgingly acknowledge that the basic arguments for it are reasonable. The main critique has shifted from “This makes no sense and I hate it” to “I hate it.”

I will not delve into the details of the Level II, III, and IV multiverses here. Read Tegmark’s book as he adroitly takes you through the details of eternal inflation, quantum mechanics and wave functions and the genius and tragic story of Hugh Everett III, the touching tribute to John Archibald Wheeler, and more, leading into a description of each multiverse level in detail.

I’d like to end this article with a quote from Max Tegmark from Mathematical Universe. It’s about when you think you’re the first person ever to discover something, only to find that someone else has made that discovery or had that idea before.

Gradually, I’ve come to totally change my feelings about getting scooped. First of all, the main reason I’m doing science is that I delight in discovering things, and it’s every bit as exciting to rediscover something as it is to be the first to discover it—because at the time of the discovery, you don’t know which is the case. Second, since I believe that there are other more advanced civilizations out there—in parallel universes if not our own—everything we come up with here on our particular planet is a rediscovery, and that fact clearly doesn’t spoil the fun. Third, when you discover something yourself, you probably understand it more deeply and you certainly appreciate it more. From studying history, I’ve also come to realize that a large fraction of all breakthroughs in science were repeatedly rediscovered—when the right questions are floating around and the tools to tackle them are available, many people will naturally find the same answers independently.

References
Ellis, G.F.R., Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Tegmark, Max. Our mathematical universe : my quest for the ultimate nature of reality. New York: Alfred A. Knopf, 2014.

“You passed your exam in many parallel universes—but not in this one.”

Why Are We Here?

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.1.6 The metaphysical options
…there appear to be basically six approaches to the issue of ultimate causation: namely Random Chance, Necessity, High Probability, Universality, Cosmological Natural Selection, and Design. We briefly consider these in turn.
Option 1: Random Chance, signifying nothing. The initial conditions in the Universe just happened, and led to things being the way they are now, by pure chance. Probability does not apply. There is no further level of explanation that applies; searching for ‘ultimate causes’ has no meaning.
This is certainly logically possible, but not satisfying as an explanation, as we obtain no unification of ideas or predictive power from this approach. Nevertheless some implicitly or explicitly hold this view.
Option 2: Necessity. Things have to be the way they are; there is no other option. The features we see and the laws underlying them are demanded by the unity of the Universe: coherence and consistency require that things must be the way they are; the apparent alternatives are illusory. Only one kind of physics is self-consistent: all logically possible universes must obey the same physics.
To really prove this would be a very powerful argument, potentially leading to a self-consistent and complete scientific view. But we can imagine alternative universes! —why are they excluded? Furthermore we run here into the problem that we have not succeeded in devising a fully self-consistent view of physics: neither the foundations of quantum physics nor of mathematics are on a really solid consistent basis. Until these issues are resolved, this line cannot be pursued to a successful conclusion.

Option 3: High probability. Although the structure of the Universe appears very improbable, for physical reasons it is in fact highly probable.
These arguments are only partially successful, even in their own terms. They run into problems if we consider the full set of possibilities: discussions proposing this kind of view actually implicitly or explicitly restrict the considered possibilities a priori, for otherwise it is not very likely the Universe will be as we see it. Besides, we do not have a proper measure to apply to the set of initial conditions, enabling us to assess these probabilities. Furthermore, application of probability arguments to the Universe itself is dubious, because the Universe is unique. Despite these problems, this approach has considerable support in the scientific community, for example it underlies the chaotic inflationary proposal. It attains its greatest power in the context of the assumption of universality:
Option 4: Universality. This is the stand that “All that is possible, happens”: an ensemble of universes or of disjoint expanding universe domains is realized in reality, in which all possibilities occur. In its full version, the anthropic principle is realized in both its strong form (if all that is possible happens, then life must happen) and its weak form (life will only occur in some of the possibilities that are realized; these are picked out from the others by the WAP, viewed as a selection principle). There are four ways this has been pursued.
1: Spatial variation. The variety of expanding universe domains is realised in space through random initial conditions, as in chaotic inflation. While this provides a legitimate framework for application of probability, from the viewpoint of ultimate explanation it does not really succeed, for there is still then one unique Universe whose (random) initial conditions need explanation. Initial conditions might be globally statistically homogeneous, but also there could be global gradients in some physical quantities so that the Universe is not statistically homogeneous; and these conditions might be restricted to some domain that does not allow life. It is a partial implementation of the ensemble idea; insofar as it works, it is really a variant of the “high probability” idea mentioned above. If it was the more or less unique outcome of proven physics, then that would provide a good justification; but the physics underlying such proposals is not even uniquely defined, much less tested. Simply claiming a particular scalar field with some specific stated potential exists does not prove that it exists!
2: Time variation. The variety of expanding universe domains could be realised across time, in a universe that has many expansion phases (a Phoenix universe), whether this occurs globally or locally. Much the same comments apply as in the previous case.
3: Quantum Mechanical. It could occur through the existence of the Everett-Wheeler “many worlds” of quantum cosmology, where all possibilities occur through quantum branching. This is one of the few genuine alternatives proposed to the Copenhagen interpretation of quantum mechanics, which leads to the necessity of an observer, and so potentially to the Strong Anthropic interpretation considered above. The many-worlds proposal is controversial: it occurs in a variety of competing formulations, none of which has attained universal acceptance. The proposal does not provide a causal explanation for the particular events that actually occur: if we hold to it, we then have to still explain the properties of the particular history we observe (for example, why does our macroscopic universe have high symmetries when almost all the branchings will not?). And above all it is apparently untestable: there is no way to experimentally prove the existence of all those other branching universes, precisely because the theory gives the same observable predictions as the standard theory.
4: Completely disconnected. They could occur as completely disconnected universes: there really is an ensemble of universes in which all possibilities occur, without any connection with each other. A problem that arises then is, What determines what is possible? For example, what about the laws of logic themselves? Are they inviolable in considering all possibilities? We cannot answer, for we have no access to this multitude of postulated worlds. We explore this further below.
In all these cases, major problems arise in relating this view to testability and so we have to query the meaningfulness of the proposals as scientific explanations. They all contradict Ockham’s razor: we “solve” one issue at the expense of envisaging an enormously more complex existential reality. Furthermore, they do not solve the ultimate question: Why does this ensemble of universes exist? One might suggest that ultimate explanation of such a reality is even more problematic than in the case of single universe. Nevertheless this approach has an internal logic of its own which some find compelling.
Option 5: Cosmological Natural Selection. If a process of re-expansion after collapse to a black hole were properly established, it opens the way to the concept not merely of evolution of the Universe in the sense that its structure and contents develop in time, but in the sense that the Darwinian selection of expanding universe regions could take place, as proposed by Smolin. The idea is that there could be collapse to black holes followed by re-expansion, but with an alteration of the constants of physics through each transition, so that each time there is an expansion phase, the action of physics is a bit different. The crucial point then is that some values of the constants will lead to production of more black holes, while some will result in less. This allows for evolutionary selection favouring the expanding universe regions that produce more black holes (because of the favourable values of physical constants operative in those regions), for they will have more “daughter” expanding universe regions. Thus one can envisage natural selection favouring those physical constants that produce the maximum number of black holes.
The problem here is twofold. First, the supposed ‘bounce’ mechanism has never been fully explicated. Second, it is not clear—assuming this proposed process can be explicated in detail—that the physics which maximizes black hole production is necessarily also the physics that favours the existence of life. If this argument could be made water-tight, this would become probably the most powerful of the multiverse proposals.
Option 6: Purpose or Design. The symmetries and delicate balances we observe require an extraordinary coherence of conditions and cooperation of causes and effects, suggesting that in some sense they have been purposefully designed. That is, they give evidence of intention, both in the setting of the laws of physics and in the choice of boundary conditions for the Universe. This is the sort of view that underlies Judaeo-Christian theology. Unlike all the others, it introduces an element of meaning, of signifying something. In all the other options, life exists by accident; as a chance by-product of processes blindly at work.
The prime disadvantage of this view, from the scientific viewpoint, is its lack of testable scientific consequences (“Because God exists, I predict that the density of matter in the Universe should be x and the fine structure constant should be y”). This is one of the reasons scientists generally try to avoid this approach. There will be some who will reject this possibility out of hand, as meaningless or as unworthy of consideration. However it is certainly logically possible. The modern version, consistent with all the scientific discussion preceding, would see some kind of purpose underlying the existence and specific nature of the laws of physics and the boundary conditions for the Universe, in such a way that life (and eventually humanity) would then come into existence through the operation of those laws, then leading to the development of specific classes of animals through the process of evolution as evidenced in the historical record. Given an acceptance of evolutionary development, it is precisely in the choice and implementation of particular physical laws and initial conditions, allowing such development, that the profound creative activity takes place; and this is where one might conceive of design taking place. [This is not the same as the view proposed by the ‘Intelligent Design’ movement. It does not propose that God tweaks the outcome of evolutionary processes.]
However from the viewpoint of the physical sciences per se, there is no reason to accept this argument. Indeed from this viewpoint there is really no difference between design and chance, for they have not been shown to lead to different physical predictions.

A few comments.

1: Random chance. At first, this strikes one as intellectual laziness, but perhaps it is more a reflection of our own intellectual weakness. More on that in a moment.

2: Necessity. Our intellectual journey of discovery and greater understanding must continue, and it may eventually lead us to this conclusion. But not now.

3: High probability. How can we talk about probability when n = 1?

4: Universality. We can hypothesize the existence of other universes, yes, but if we have no way to observe or interact with them, how can we call this endeavor science? Furthermore, explaining the existence of multiple universes seems even more problematic that explaining the existence of a single universe—ours.

5: Cosmological Natural Selection. We do not know that black holes can create other universes, or that universes that contain life are more likely to have laws of physics that allow an abundance of black holes

First image of a black hole by the Event Horizon Telescope. The object M87* is located at the heart of galaxy Messier 87, about 54 million light years distant. The mass of this supermassive black hole is estimated at 6.5 billion solar masses.

6. Purpose of Design. The presupposition of design is not evidence of design. It is possible that scientific evidence of a creator or designer might be found in nature—such as an encoded message evincing purposeful intelligence in DNA or the cosmic microwave background—but to date no such evidence has been found. Even if evidence of a creator is forthcoming, how do we explain the existence of the creator?

I would now like to suggest a seventh option (possibly a variant of Ellis’s Option 1 Random Chance or Option 2 Necessity).

7. Indeterminate Due to Insufficient Intelligence. It is at least possible that there are aspects of reality and our origins that may be beyond what humans are currently capable of understanding. For some understanding of how this might be possible, we need look no further than the primates we are most closely related to, and other mammals. Is a chimpanzee self-aware? Can non-humans experience puzzlement? Are animals aware of their own mortality? Even if the answer to all these questions is “yes”1, there are clearly many things humans can do that no other animal is capable of. Why stop at humans? Isn’t it reasonable to assume that there is much that humans are cognitively incapable of?

Why do we humans develop remarkable technologies and yet fail dismally to eradicate poverty, war, and other violence? Why does the world have so many religions if they are not all imperfect and very human attempts to imbue our lives with meaning?

What is consciousness? Will we ever understand it? Can we extrapolate from our current intellectual capabilities to a complete understanding of our origins and the origins of the universe, or is something more needed that we currently cannot even envision?

“Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.” —Brian Greene, The Elegant Universe

“To ask what happens before the Big Bang is a bit like asking what happens on the surface of the earth one mile north of the North Pole. It’s a meaningless question.” —Stephen Hawking, Interview with Timothy Ferris, Pasadena, 1985

1 For more on the topic of the emotional and cognitive similarities between animals and humans, see “Mama’s Last Hug: Animal Emotions and What They Tell Us about Ourselves” by primatologist Frans de Waal, W. W. Norton & Company (2019). https://www.amazon.com/dp/B07DP6MM92 .

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

The Laws of Physics and the Existence of Life

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

The first requirement is the existence of laws of physics that guarantee the kind of regularities that can underlie the existence of life.  These laws as we know them are based on variational and symmetry principles; we do not know if other kinds of laws could produce complexity.  If the laws are in broad terms what we presently take them to be, the following inter alia need to be right, for life of the general kind we know to exist:

  • Quantization that stabilizes matter and allows chemistry to exist through the Pauli exclusion principle.

  • The neutron-proton mass differential must be highly constrained.  If the neutron mass were just a little less than it is, proton decay could have taken place so that by now no atoms would be left at all.

  • Electron-proton charge equality is required to prevent massive electrostatic forces overwhelming the weaker electromagnetic forces that govern chemistry.

  • The strong nuclear force must be strong enough that stable nuclei exist; indeed complex matter exists only if the properties of the nuclear strong force lies in a tightly constrained domain relative to the electromagnetic force.

  • The chemistry on which the human body depends involves intricate folding and bonding patterns that would be destroyed if the fine structure constant (which controls the nature of chemical bonding) were a little bit different.

  • The number D of large spatial dimensions must be just 3 for complexity to exist.

It should not be too surprising that we find ourselves in a universe whose laws of physics are conducive to the existence of semi-intelligent life.  After all, we are here.  What we do not know—and will probably never know: Is this the only universe that exists?  This is an important question, because if there are many universes with different laws of physics, our existence in one of them may be inevitable.  If, on the other hand, this is the only universe, then the fantastic claims of the theists, or at least the deists, become more plausible.

You may wonder why I call the human race semi-intelligent.  Rest assured, I am not being sarcastic or sardonic.  I say “semi-intelligent” to call attention to humanity’s remarkable technological and scientific achievements while also noting our incredible ineptness at eradicating war, violence, greed, and poverty from the world.  What is wrong with us?

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Lost in Math: A Book Review

I recently finished reading a thought-provoking book by theoretical physicist Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray. Hossenfelder writes in an engaging and accessible style, and I hope you will enjoy reading this book as much as I did. Do we have a crisis in physics and cosmology? You be the judge. She presents convincing arguments.

The basic premise of Hossenfelder’s book is that when theoretical physicists and cosmologists lack empirical data to validate their theories, they have to rely on other approaches—”beauty”, “symmetry”, “simplicity”, “naturalness“, “elegance”—mathematics. Just because these approaches have been remarkably successful in the past is no guarantee they will lead to further progress.

One structural element that contributes to the book’s appeal is Hossenfelder’s interviews with prominent theoretical physicists and cosmologists: Gian Francesco Giudice, Michael Krämer, Gordon Kane, Keith Olive, Nima Arkani-Hamed, Steven Weinberg, Chad Orzel, Frank Wilczek, Garrett Lisi, Joseph Polchinski, Xiao-Gang Wen, Katie Mack, George Ellis, and Doyne Farmer. And, throughout the book, she quotes many other physicists, past and present, as well. This is a well-researched book by an expert in the field.

I also like her “In Brief” summaries of key points at the end of each chapter. And her occasional self-deprecating, brief, soliloquies, which I find reassuring. This book is never about the care and feeding of the author’s ego, but rather giving voice to largely unspoken fears that theoretical physics is stagnating. And an academic environment hell-bent on preserving the status quo isn’t helping matters, either.

Anthropic Principle

Do we live in a universe fine-tuned for life? If so, is it the only possible universe that would support life? Recent work indicates that there may be more than one set of parameters that could lead to a life-supporting universe.

Beauty is in the Eye of the Beholder

Is our sense of what is “beautiful” a reliable guide to gaining a deeper understanding of nature? Or does it sometimes lead us astray? We know from history that it does.

In the past, symmetries have been very useful. Past and present, they are considered beautiful

When we don’t have data to guide our theory development, aesthetic criteria are used. Caveat emptor.

Experiment and Theory

Traditionally, experiment and observation have driven theory. Now, increasingly, theory drives experiment, and the experiments are getting more difficult, more expensive, and more time consuming to do—if they can be done at all.

Inflation

The rapid expansion of the universe at the time of the Big Bang is known as cosmic inflation, or, simply, inflation. Though there is some evidence to support inflation, that evidence is not yet compelling.

Mathematics

Mathematics creates a logically consistent universe all its own. Some of it can actually be used to describe our physical universe. What math is the right math?

Math is very useful for describing nature, but is math itself “real”, or is it just a useful tool? This is an ancient question.

Memorable Quotations

“I went into physics because I don’t understand human behavior.” (p. 2)

“If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.” (p. 9)

“In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.” (p. 10)

On artificial intelligence: “Being unintuitive shouldn’t be held against a theory. Like lack of aesthetic appeal, it is a hurdle to progress. Maybe this one isn’t a hurdle we can overcome. Maybe we’re stuck in the foundations of physics because we’ve reached the limits of what humans can comprehend. Maybe it’s time to pass the torch.” (p. 132)

“The current organization of academia encourages scientists to join already dominant research programs and discourages any critique of one’s own research area.” (p. 170)

Multiverse

The idea that our universe of just one of a great many universes is presently the most controversial idea in physics.

Particles and Interactions

What is truly interesting is not the particles themselves, but the interactions between particles.

Philosophy

Physicists and astrophysicists are sloppy philosophers and could stand to benefit from a better understanding of the philosophical assumptions and implications of their work.

Physics isn’t Math

Sure, physics contains a lot of math, but that math has traditionally been well-grounded in observational science. Is math driving physics more than experiment and observation today?

Quantum Mechanics

Nobody really understands quantum mechanics. Everybody’s amazed but no one is happy. It works splendidly well. The quantum world is weird. Waves and particles don’t really exist, but everything (perhaps even the universe itself) is describable by a probabilistic “wave function” that has properties of both and yet is neither. Then there’s the many-worlds interpretation of quantum mechanics, and quantum entanglement

Science and the Scientific Method

In areas of physics where experiments are too difficult, expensive, or impossible to do, some physicists seem to be abandoning the scientific method as the central pillar of scientific inquiry. Faith in beauty, faith in mathematics, faith in naturalness, faith in symmetry. How is this any different than religion?

If scientists can evaluate a theory using other criteria than that theory’s ability to describe observation, how is that science?

Stagnation

Some areas of physics haven’t seen any new data for decades. In such an environment, theories can and do run amok.

Standard Model (of particle physics)

Ugly, contrived, ad hoc, baroque, overly flexible, unfinished, too many unexplained parameters. These are some of the words used to describe the standard model of particle physics. And, yet, the standard model describes the elementary particles we see in nature and their interactions with extraordinary exactitude.

String Theory

String theory dates back at least to the 1970s, and its origins go back to the 1940s. To date, there is still no experimental evidence to support it. String theory is not able to predict basic features of the standard model. That’s a problem.

Triple Threat: Crises in Physics, Astrophysics, and Cosmology?

Physics: Sure, the Large Hadron Collider (LHC) at CERN gave us the Higgs boson, but little else. No new physics. No supersymmetry particles. Embarrassments like the diphoton anomaly. Do we need a bigger collider? Perhaps. Do we need new ideas? Likely.

Astrophysics: We’ve spent decades trying to understand what dark matter is, to no avail. No dark matter particles have been found.

Cosmology: We have no testable idea as to what dark energy is. Plenty of theories, though.


See Hossenfelder’s recent comments on the LHC and dark matter in her op-ed, “The Uncertain Future of Particle Physics” in the January 23, 2019 issue of The New York Times.


The book concludes with three appendices:

  • Appendix A: The Standard Model Particles
  • Appendix B: The Trouble with Naturalness
  • Appendix C: What You Can Do To Help

Hossenfelder gives some excellent practical advice in Appendix C. This appendix is divided into three sections of action items:

  • As a scientist
  • As a higher ed administrator, science policy maker, journal editor, or representative of a funding body
  • As a science writer or member of the public

I’m really glad she wrote this book. As an insider, it takes courage to criticize the status quo.

References
Hossenfelder, S., Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018).
Hossenfelder, Sabine. “The Uncertain Future of Particle Physics.” The New York Times 23 Jan 2019. https://www.nytimes.com/2019/01/23/opinion/particle-physics-large-hadron-collider.html.

The Anthropic Question

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.1 Issue G: The anthropic question: Fine tuning for life
One of the most profound fundamental issues in cosmology is the Anthropic question: why does the Universe have the very special nature required in order that life can exist?  The point is that a great deal of “fine tuning” is required in order that life be possible.  There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible; in particular various fundamental constants are highly constrained in their values if life as we know it is to exist:

Ellis goes on to quote Martin Rees.

A universe hospitable to life—what we might call a biophilic universe—has to be special in many ways … Many recipes would lead to stillborn universes with no atoms, no chemistry, and no planets; or to universes too short lived or too empty to evolve beyond sterile uniformity.

Physics does not tell us anything (yet) about why the fundamental constants and other parameters have the values they do.  These parameters include, for example, the speed of light, the Planck constant, the four fundamental forces and their relative strengths, the mass ratio of the proton and the electron, the fine-structure constant, the cosmological density parameter, Ωtot, relative to the critical density, and so on.  And, why are there four fundamental forces?  Why not five?  Or three?

Also, why do we live in a universe with three spatial dimensions and one time dimension?  Others are possible—even universes with two or more time dimensions.

But it appears that only three spatial dimensions and one time dimension is conducive to life (at least life as we know it), as shown in the diagram above (Whittle 2008).

In fact, altering almost any of the parameters would lead to a sterile universe and we could not exist.  Is the universe fine-tuned for our existence?

Let’s assume for the moment it is.  Where does that lead us?

  1. As our understanding of physics advances, we will eventually understand why these parameters must have the values that they do. -or-
  2. We will eventually learn that some of these parameters could have been different, and still support the existence of life. -or-
  3. God created the universe in such a way that life could exist -or-
  4. We’re overthinking the problem.  We live in a life-supporting universe, so of course we find the parameters are specially tuned to allow life. -or-
  5. There exist many universes with different parameters and we just happen to find ourselves in one that is conducive to life. (The multiverse idea.)

#4 is the anthropic explanation, but a deeper scientific understanding will occur if we find either #1, #2, or #5 to be true.  #3 is problematic for a couple of reasons.  First of all, how was God created?  Also, deism has a long history of explaining phenomena we don’t understand (“God of the gaps”), but in time we are able to understand each phenomenon in turn as science progresses.

The anthropic explanation itself is not controversial.  What is controversial is deciding to what degree fine tuning has occurred and how to explain it.

In recent years, the multiverse idea has become more popular because, for example, if there were a billion big bangs and therefore a billion different universes created, then it should not be at all surprising that we find ourselves in  one with just the right set of parameters to allow our existence.  However, there is one big problem with the multiverse idea.  Not only do we have no physical evidence that a multiverse exists, but we may never be able to obtain evidence that a multiverse exists, due to the cosmological horizon problem1.  If physical evidence of a multiverse is not forthcoming, then in that sense it is not any better than the deistic explanation.

To decide whether or not there is only one combination of parameters that can lead to life we need to rule out all the other combinations, and that is a tall order.  Recent work in this field suggests that there is more than one combination of parameters that could create a universe that is hospitable to life (Hossenfelder 2018).

Thinking now about why our universe is here at all, it seems there are just two possibilities:

(1)  Our universe has a supernatural origin.

(2)  Our universe has a natural origin.

If our universe has a supernatural origin, then what is the origin of the supernatural entity (e.g. God)?  If, on the other hand, our universe had a natural origin (e.g. something was created out of nothing), didn’t something have to exist (laws of physics or whatever) before the universe came into existence?  If so, what created those pre-conditions?

In either case, we are facing an infinite regression.  However, we could avoid the infinite regression by stating that something has to exist outside of time, that is to say, it has no beginning and no ending.  But isn’t this just replacing one infinity with another?

Perhaps there’s another possibility.  Just as a chimpanzee cannot possibly understand quantum mechanics, could it be that human intellect is also fundamentally limited?  Are the questions in the previous two paragraphs meaningless or nonsensical in the context of some higher intelligence?

1We appear to live in a universe that is finite but very much larger than the region that is visible to us now, or ever.

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (Basic Books, 2018).

M. J. Rees, Our Cosmic Habitat (Princeton and Oxford, 2003).

Mark Whittle, “Fine Tuning and Anthropic Arguments”, Lecture 34, Course No. 1830.  Cosmology: The History and Nature of Our Universe.  The Great Courses, 2008.  DVD.
[https://www.thegreatcourses.com/courses/cosmology-the-history-and-nature-of-our-universe.html]

Observation, Theory, and Reality

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

8.3 Limits of Representation and Knowledge of Reality
It follows…that there are limits to what the scientific method can achieve in explanatory terms.  We need to respect these limits and acknowledge clearly when arguments and conclusions are based on some philosophical stance rather than purely on testable scientific argument.  If we acknowledge this and make that stance explicit, then the bases for different viewpoints are clear and alternatives can be argued about rationally.

We human beings want so badly to be able to explain our existence and existence itself that we tend to “fill in the blanks” and treat speculation (no matter how well reasoned) as if it were something akin to fact.  This is true for both science and religion.  A more reasonable approach, it seems to me, is to reject absolute certainty—especially where physical evidence is sparse or nonexistent—while always striving to deepen our understanding.  That is the scientist’s stock-in-trade—or should be.  Each of us needs to become more aware of the limitations of our understanding!

Thesis F6: Reality is not fully reflected in either observations or theoretical models.
Problems arise from confusion of epistemology (the theory of knowledge) with ontology (the nature of existence): existence is not always manifest clearly in the available evidence.  The theories and models of reality we use as our basis for understanding are necessarily partial and incomplete reflections of the true nature of reality, helpful in many ways but also inevitably misleading in others.  They should not be confused with reality itself!

We humans create our own “realities”, but under the very best of circumstances (science, for example), our “reality” is only an imperfect model of what actually exists.

The confusion of epistemology with ontology occurs all the time, underlying for example the errors of both logical positivism and extreme relativism.  In particular, it is erroneous to assume that lack of evidence for the existence of some entity is proof of its non-existence.  In cosmology it is clear for example that regions may exist from which we can obtain no evidence (because of the existence of horizons); so we can sometimes reasonably deduce the existence of unseen matter or regions from a sound extrapolation of available evidence (no one believes matter ends at or just beyond the visual horizon).  However one must be cautious about the other extreme, assuming existence can always be assumed because some theory says so, regardless of whether there is any evidence of existence or not.  This happens in present day cosmology, for example in presentations of the case for multiverses, even though the underlying physics has not been experimentally confirmed.  It may be suggested that arguments ignoring the need for experimental/observational verification of theories ultimately arise because these theories are being confused with reality, or at least are being taken as completely reliable total representations of reality.

Absence of evidence is not evidence of absence.  But, without evidence, all we have is conjecture, no matter how well informed.  As Carl Sagan once said, “Extraordinary claims require extraordinary evidence.”

No model (literary, intuitive, or scientific) can give a perfect reflection of reality.  Such models are always selective in what they represent and partial in the completeness with which they do so.  The only model that would reflect reality fully is a perfect fully detailed replica of reality itself! This understanding of the limits of models and theories does not diminish the utility of these models; rather it helps us use them in the proper way.  This is particularly relevant when we consider how laws of nature may relate to the origins of the universe itself, and to the existence and nature of life in the expanding universe.  The tendency to rely completely on our theories, even when untested, seems sometimes to arise because we believe they are the same as reality—when at most they are descriptions of reality.

Ellis makes a pretty good case here against dogma.  Though he does not specifically mention religion (and why should he, as the subject at hand is cosmology), I do think these ideas apply to religion as well.

Always a journey, never a destination.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Theory and Observation

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis F1: Philosophical choices necessarily underly cosmological theory.
Some cosmologists tend to ignore the philosophical choices underlying their theories; but simplistic or unexamined philosophical standpoints are still philosophical standpoints!

Cosmology, and indeed all human inquiry, is based on (at least) two unproven (though certainly reasonable) assumptions:

  1. The Universe exists.
  2. The human mind is at least to some degree capable of perceiving and understanding the Universe.

Any cosmological theory will have additional foundational unproven assumptions.  These are called axioms.  Ellis admonishes us to at least be aware of them, and to admit to them.

8.1 Criteria for theories
As regards criteria for a good scientific theory, typical would be the following four areas of assessment: (1) Satisfactory structure: (a) internal consistency, (b) simplicity (Ockham’s razor), and (c) aesthetic appeal (‘beauty’ or ‘elegance’); (2) Intrinsic explanatory power: (a) logical tightness, (b) scope of the theory—the ability to unify otherwise separate phenomena, and (c) probability of the theory or model with respect to some well-defined measure; (3) Extrinsic explanatory power, or relatedness: (a) connectedness to the rest of science, (b) extendability—providing a basis for further development; (4) Observational and experimental support, in terms of (a) testability: the ability to make quantitative as well as qualitative predications that can be tested; and (b) confirmation: the extent to which the theory is supported by such tests as have been made.

As you can see, a theory is not an opinion.  It must be well-supported by facts.  It must be internally consistent.  It must have explanatory power.  The Russian physicist A. I. Kitaĭgorodskiĭ (1914-1985) put it succinctly: “A first-rate theory predicts; a second-rate theory forbids, and a
third-rate theory explains after the event.”  Einstein’s special and general relativity are spectacular examples of first-rate theories.  In over 100 years of increasingly rigorous and sophisticated experiments and observations, relativity has never been proven to be incorrect.

Ellis emphasizes the importance of observational and experimental support in any scientific theory.

It is particularly the latter that characterizes a scientific theory, in contrast to other types of theories claiming to explain features of the universe and why things happen as they do.  It should be noted that these criteria are philosophical in nature in that they themselves cannot be proven to be correct by any experiment.  Rather their choice is based on past experience combined with philosophical reflection.  One could attempt to formulate criteria for good criteria for scientific theories, but of course these too would need to be philosophically justified.  The enterprise will end in infinite regress unless it is ended at some stage by a simple acceptance of a specific set of criteria.

So, even our criteria about what makes a good scientific theory rest upon axioms that cannot be proven.  But unlike religion, scientific theories never posit the existence of any supernatural entity.

Thesis F3: Conflicts will inevitably arise in applying criteria for satisfactory cosmological theories.
The thrust of much recent development has been away from observational tests toward strongly theoretically based proposals, indeed sometimes almost discounting observational tests.  At present this is being corrected by a healthy move to detailed observational analysis of the consequences of the proposed theories, marking a maturity of the subject.  However because of all the limitations in terms of observations and testing, in the cosmological context we still have to rely heavily on other criteria, and some criteria that are important in most of science may not really make sense.

String theory? Cosmic inflation?  Multiverse? If a theory is currently neither testable nor directly supported by observations, is it science, or something else?

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

What Is and What Might Have Been

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis E2: We cannot take the nature of the laws of physics for granted.
One cannot take the existence and nature of the laws of physics (and hence of chemistry) as unquestionable in cosmology—which seems to be the usual habit in biological discussions on the origin and evolution of life.  This is in stark contrast to the rest of science, where we are content to take the existence and nature of the laws describing the fundamental behaviour of matter as given and unchangeable.  Cosmological investigation is interested in the properties of hypothetical universes with different physical behaviour.  Consideration of ‘what might have been’ is a useful cosmological speculation that may help throw light on what actually is; this is a statement of the usefulness of ‘Gedanken experiments‘ in cosmology.

Practical science, engineering, and technology are prescriptive.  If we do a, we know from experience that b will occur.  Using the laws of physics, we can predict the location of the Moon as a function of time, put a spacecraft in orbit around Saturn, or build a light bulb that will illuminate.  Though we may be curious, we are not required to know why or how these laws exist—or how they might have been different—only that they do work, time and time again.

Cosmology, though firmly rooted in science, is different.  We are passive observers in a very large and very old universe, and there is no absolute guarantee that the laws of physics that work for us so well in the here and now apply to all places and at all times.  We must attempt to understand the laws of physics in a larger context that does involve some well-reasoned and reasonable speculation.

“Not only does God … play dice, but He sometimes confuses us by throwing them where they can’t be seen.” – Stephen Hawking

“Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.” – Brian Greene

In politics, governance, sociology, and philosophy, too, I would submit to you that consideration of “what might have been” is useful in helping us to understand what actually is.  Such reflection, en masse, might even lead to substantive change.

“Why is it that here in the United States we have such difficulty even imagining a different sort of society from the one whose dysfunctions and inequalities trouble us so?  We appear to have lost the capacity to question the present, much less offer alternatives to it.  Why is it so beyond us to conceive of a different set of arrangements to our common advantage?” – Tony Judt

Getting back to cosmology, however, for the moment…

Indeed if one wants to investigate issues such as why life exists in the universe, consideration of this larger framework—in essence, a hypothetical ensemble of universes with many varied properties—is essential (this is of course not the same as assuming an ensemble of such universes actually exists).  However, we need to be very cautious about using any claimed statistics of universes in such a hypothetical ensemble of all possible or all conceivable universes.  This is usually not well defined, and in any case is only relevant to physical processes if either the ensemble actually exists, rather than being a hypothetical one, or if it is the outcome of processes that produce well-defined probabilities—an untestable proposal.  We can learn from such considerations the nature of possible alternatives, but not necessarily the probability with which they might occur (if that concept has any real meaning).

It is easy to imagine a universe without life.  But we obviously do not live in such a universe.  There may be other universes devoid of life.

For the more thoughtful among us, it is easy to imagine a civilization without war, guns, violence, extrinsic suffering1 caused by others, or deprivation.  Obviously, we do not live in such a society.  But how can we say it is impossible, or even improbable?  It would be easy to find many millions of people in the world even today that would never fight in a war, would never own or use a gun, who would never resort to violence, who would never cause others to suffer, and who would make eliminating deprivation and poverty a top priority.  The question for the scientists is: what is wrong with the rest of us?

1Extrinsic suffering is suffering caused by others or circumstances completely outside of one’s control.  Intrinsic suffering, on the other hand, is self-inflicted—through our own failings, poor judgement, or mistakes that we make.

Growing Older

As we grow older,
That which is older grows upon us.
Time accelerates,
And the world seems a smaller place.

The years go by like months,
The months go by like weeks,
The weeks go by like days,
The days go by like hours,
And the hours go by like minutes.

And our world which in our youth was all that we knew
Slowly reveals itself to be a surprisingly alien place,
Full of centuries of hard work, unlikely events, and compromise:
The world could be a very different (and better) place,
Even within the confines of human nature.

Taken to its natural conclusion
Were we each to live for millennia, perhaps longer
We would find eternity in an instant
And infinity at the door.

David Oesper

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]