Welcome to Our Blog on Philosophy of Cosmology
Welcome to our blog on philosophy of cosmology. Herein you will find discussions of issues in philosophy of cosmology, developments in cosmology and fundamental physics, and more generally philosophy of physics and philosophy of science and sometimes discussions about what it all means. The Bloggers are members of a group of philosophers and physicists (see main page) who are involved in a 3 year project supported by the Templeton Foundation and whose research includes cosmology, string theory, philosophy of physics, metaphysics, philosophy of religion and related fields. In addition there will be invited guest bloggers and commentators whose work and interests appropriately intersect with our group. We are aiming to produce lively, informed, and philosophically interesting discussions.
Among the questions in philosophy of cosmology which we are interested in addressing are:
1) Does the low entropy condition of the universe at the Big Bang (what is often called the “past hypothesis” or “PH”) require explanation? How successful are attempts to explain it?
2) Was there anything “before” the Big Bang?
3) Is our universe one among many? What scientific and philosophical reasons are there for “many universes” and “bubble universes” hypotheses?
4) What does the apparent fine tuning of the laws and initial conditions of the universe imply about the origin of the universe and about the existence of many universes?
5) What is the meaning and metaphysics of probability in the context of fundamental physical and cosmological theories?
6) How should the cosmological constant and dark energy be understood?
7) What are the connections between cosmology, statistical mechanics, and time’s arrows?
8) Does “the wave function of the universe as a whole” make sense? What is its “ontological status?”
9) How do the interpretational problems in quantum mechanics (“the measurement”) interact with issues in cosmology? How should the non-local influences found in QM be understood?
10) How does the physical description of the universe relate to the physical states of its constituents? Is there support for a Spinozistic conception of the universe on which the whole is metaphysically prior to the parts?
11) Does the uniqueness of the universe pose special epistemological problems especially regarding the nature of probability and statistical reasoning?
12) What are the metaphysical natures of fundamental laws and fundamental chances?
13) Why is there something rather than nothing?
I imagine that all of these will be discussed during the course of our project. However, I suggest holding off definitively answering question 13 until our grant has expired.
I would like to start our discussions off with question #1 above since I know that our group represents various views about it.
Roger Penrose has said that the question of what, if anything, explains why 13.7 billion years ago the universe was in a very special state (“the Big Bang”) is one of the most important and puzzling questions facing the foundations of physics. In a recent article our colleague Tim Maudlin remarked that ‘This question of accounting for what we call the “big bang state” is probably the most important question within the philosophy of cosmology”.
The BB state is “special” (quite unlike the universe we see around us now) in that its volume was tiny, and its density, pressure and temperature immense. But according to Penrose what makes it especially in need of explaining is that its entropy was incredibly low. The low entropy of the BB state is a conclusion of inferences based on observational astronomy and also a hypothesis that grounds (and seems to be required to ground) the second law of thermodynamics and arguably also is implicated in various other temporal asymmetries (the asymmetries of records and influence). How that works or is supposed to work will be discussed and argued over in future blog entries. The low entropy of the BB state means that the set of micro states that realize the BB condition occupies a minute portion of the phase space of possible states; so small that were we to suppose (as Penrose suggests) that the actual state was selected at random from the set of all physically possible states (given the mass energy of the universe) the chance of selecting a state with the Big Bang conditions is, Penrose calculates, 1 over 10^10^123. Penrose thinks that since the BB state is so unlikely it cries out for an explanation. Among the suggestions one can find are
1. The universe was created in the BB state by a designer.
2. The universe is infinite and unbounded in both temporal directions and is typically in equilibrium. The BB state came about as a very unlikely fluctuation. While it is very unlikely to find the universe in a low entropy state in any finite temporal interval it is very likely (probability 1) that in the infinite history of our universe that there are such (infinitely many in fact) such fluctuations. (Boltzmann might suggest this.)
3. Multiverse hypotheses. For example, Sean Carroll has proposed an account which roughly says that our universe was cleaved off from a “mother universe” whose state is typical and which produces “baby universes” in BB like states.
4. The intuition that the BB state “cries out” for explanation is based on a mistaken use of probability. There is no more need to explain the low entropy BB state than to explain the dynamical laws. (Of course this is not to reject the possibility of explaining the BB state).
1 and 2 are probably non-starters for well known reasons (1 since it really isn’t an explanation and 2 for reasons that Feynman and others have pointed out). It is unclear how to me whether Carroll’s account works or even if the fundamental laws are as he hopes it works. Here is a link to a very nice talk he gave to Google (the company) that explains it. I am interested in developing 4 since it goes along nicely with the Lewisian account of laws and objective probabilities that I like. But even after persuading myself of that account (I am sure we will discuss and argue about the nature of chances and laws in future blog entries) there still feels like there is an itch that needs scratching. Anyway, I am curious what you all think about Penrose’s problem.
What There Is and Why There Is Anything 
Can you explain the difference between cosmology (looking for what is/was/will be out there) and the philosophy of cosmology?
Dear Louis:
Cosmology, as you’ve defined it, is patently a metaphysical field of research, due to the implicit assumption that there really is something “out there”, and the hope for an explanation of what it is, and why it should be that way, rather than only the search for an accurate empirical model to describe appearances. In “looking for what is/was/will be out there”, we might (1) conduct experiments in order to determine empirical facts, (2) begin with some hypotheses and work through the accidental mathematics in order to synthesise a theory that might eventually be verified by experiment, thus indicating that those hypotheses might be correct, or (3) begin with the whole picture, combining the empirical facts and confirmed hypotheses that we do know, and work through analytically to determine how each of its parts should best fit together, so that we can attempt to refine those initial hypotheses and use that knowledge to develop a theory that could better explain the facts of experience. Typically, we refer to (1) as experimental physics, (2) as theoretical physics, and (3) as philosophy of physics; and each is a subfield of the greater field of metaphysical research.
Maxwell’s theory of electromagnitism provides an excellent example of how this all works, and how important the philosophical aspect can be in theoretical development. As he wrote in the preface to his Treatise on Electricity and Magnetism (1873), “I have . . . thought that a treatise would be useful which should have for its principal object to take up the whole subject in a methodical manner, and which should also indicate how each part of the subject is brought within the reach of methods of verification by actual measurement. . . . When I had translated what I considered to be Faraday’s ideas into a mathematical form, I found that in general the results of [both his methods and the ordinary ones] coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday’s methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis. . . . The great success which . . . eminent men have attained in the application of mathematics to electrical phenomena, gives, as is natural, additional weight to their theoretical speculations, so that those who, as students of electricity, turn to them as the greatest authorities in mathematical electricity, would probably imbibe, along with their mathematical methods, their physical hypotheses. These physical hypotheses, however, are entirely alien from the way of looking at things which I adopt . . .”
As regards cosmology, there have been no fundamental advances in the standard model (GRT+RW background structure) for about eighty years. The reason for this, is that the theory applies so well as a generally applicable empirical model, so that it has been extremely successful in that regard, especially in the past decade. The problem, however, is that the universe of empirical constraint is almost completely at odds with all of our expectations. Therefore, because a lot of knowledge has been gained since the basic theory was developed, a philosophical approach to the problem might be to begin with an analysis of what is known, in order to determine the extent to which each part of the theory remains justified, and attempt to infer new hypotheses that could eventually be used to better explain things within a self-consistent theory. For, as Einstein (1916) put it, “What is essential, which is based solely on accidents of development? . . . It is . . . by no means an idle trifling, if we become practiced in analysing the long-familiar concepts, and show upon which circumstances their justification and applicability depend, as they have grown up, individually, from the facts of experience.”
Regards,
Daryl
Barry, can you say a bit more about why Feynman and others would reject 2 or provide a link?
to arete:
Feynman’s objection to the fluctuation hypothesis, which originates in a paper of Boltzmann (but maybe not with Boltzmann himself) is that if the low-entropy state were the result of a fluctuation, and one uses the standard formalism to calculate the probability of various fluctuations, then it is overwhelming most probable that it would be a minimal fluctuation, that is, a fluctuation with the greatest entropy sufficient to produce the universe we see around us. But given such a minimal fluctuation, we would then make certain sorts of predictions about the not-yet-observed parts of the universe, namely, that they should be in equilibrium. (Having them not be in equilibrium requires an even deeper fluctuation than the minimal one that accounts for what we have yet observed). So the fluctuation hypothesis entails a prediction: if you look somewhere in the universe that you haven’t checked yet (point the telescopes in a new direction), instead of seeing starts, galaxies, etc. you should see equilibrium. But you never do. So the fluctuation hypothesis is almost certainly false.
Does this also exclude any view on which the universe has a beginning but is temporally infinite in the forwards direction and tends towards an equilibrium state, unless that equilbrium state is such that fluctuations from the equilibrium state to a state like ours have probability zero?
No, it does not exclude the view, but the same argument seems to show that we have very strong reason to think that we are in the initial part of such a universe. If we accept Feynman’s argument, then it is empirically highly unlikely that our low-entropy Big Bang state (i.e. the lowest entropy state one encounters following a downward-sloping entropy gradient from now) is a fluctuation and was preceded by a much higher-entropy state. The probability of what we see conditional on the hypothesis that we are in the initial period of such a world is much higher than the probability conditional on the fluctuation hypothesis. Now if time is really infinite in the forward direction, and the phase space available to the whole universe is bounded, then there are complications…but I don’t know of any cosmological models that suggest this.
I am afraid I don’t see it.
A universe like the one I describe is going to have an infinite number of fluctuations into a state very similar to the our present state of the universe (since it spends infinitely long close to equilibrium and I have assumed it has non-zero probability of fluctuating into a state very much like ours–I did mean here a universe-state like that which we now have). But once the universe is in a state very much like ours, its forward evolution will very likely be very much like the forward evolution of our state. The dynamics is memoryless, I assume, so it doesn’t matter for the forward evolution whether the state came from an earlier even lower entropy state or was the bottom of a fluctuation.
So there are going to be infinitely many downward fluctuations where the observers observe pretty much what we observe. Why would there then be reason to think we’re in the initial part of such a universe?
“The probability of what we see conditional on the hypothesis that we are in the initial period of such a world is much higher than the probability conditional on the fluctuation hypothesis.”
Distinguish two fluctuation hypotheses: H1 = We are in a fluctuation to a global state like we think the universe is in. H2 = We are in a fluctuation to a state that includes our observations. And then let J be the hypothesis that we’re in the initial part. Then I think the Feynman argument shows that we’ve got strong confirmation of J over H2, but H1 (which entails H2) seems to remain more probable than J in the scenario.
I am bracketing nasty issues with infinite lotteries which might sink the whole line of thought.
I don’t want to presume how this conversation might emerge but am wondering if there is going to be a structure to the discussions. For example are the subtopics going to be characterized by some “central group” and then discussion ensues? Will subject matter experts post positions on these to lead to conversations. Are commenters allowed/encouraged to submit threads for discussion etc. Perhaps these are still unknowns at this point but I am excited about the possibilities here and wonder how things might unfold.
Right after putting up the first discussion I came down with a flu. Thanks for the comments so far. I would like to keep this discussion focused on the topic and will make a few remarks tomorrow. For now can I ask each person who comments to identify themselves (no anonymous comments) saying who, where etc
feverishly
Barry
This blog is going to consist of regular posts by leaders in the field of philosophy of cosmology. Questions and comments are encouraged, both on posts as well as other comments, though our policy is to post only those that we feel will significantly further the discussion. Additionally, the comments are organized in a nesting structure, allowing for distinct threads under a single post.
“1 … really isn’t an explanation”
I see two main reasons why one might deny that 1 is an explanation. The first is to claim 1 isn’t true and explanations have to be true. The second is to claim that 1 isn’t the sort of thing that would be an explanation even if it were true. The first begs the question, so let’s take up the second.
Suppose for the sake of discussion that 1 is true (and in fact I think 1 is true). Is 1 an explanation? Well, I think it depends on whether “Jones was killed by somebody” is an explanation of why Jones died when in fact Jones was killed by somebody. If “Jones was killed by somebody” is an explanation of why Jones died when it is true, then by the same token “The universe was created in the BB state by a designer” should be an explanation of why the universe started in the BB state when it is true. I am inclined to think “Jones was killed by somebody” really is an explanation of why Jones died, just one that isn’t as informative as we’d like. We’d like to hear a bit more about who the killer is, what methods the killer used and what motives the killer had.
But I could see somebody saying that “Jones was killed by somebody” isn’t an explanation even if true, only being a gesture in the direction of an explanation, where the real explanation is more informative. If one says that, I think one should say the same thing about 1. But then that doesn’t dismiss 1 from the options to be considered in trying to find an explanation of the BB state, just as “Jones was killed by somebody” shouldn’t be dismissed from the options to be considered in trying to find an explanation of Jones’ death just because one hasn’t indicated who would have done it, how and why. Rather, we should see if we can fill in that detail.
And of course there is at least one concrete proposal that fills in the details for 1, namely the classic theist view:
1a. There is a necessarily existent being who has the power to create any coherent physical configuration the being wishes, and who is motivated to create a configuration S in proportion to the objective value of creating S, and this being created a universe in the BB state because of the objective value of a universe starting in the BB state.
Of course that doesn’t end things. For instance, it’s not an easy question to figure out what sort of objective value a universe starting in the BB state has. One can ask whether it’s an instrumental or non-instrumental value. Whether it is aesthetic, moral or some other kind of value. One can query whether it is plausible that the universe’s starting in the BB state would in fact have any significant value at all. But that a putative explanation leads to such further questions is not something that counts against its status as a putative explanation. And it sure seems that 1a is an explanation of why the universe started in the BB state if 1a is true.
By the way, for the sake of completeness, there is also the John Leslie / Nicholas Rescher view that it is a fundamental principle that everything is for the best. This might give a value-based explanation of the BB state that need not necessarily depend on a designer. (In fact, Rescher thinks there is a God whose existence is explained by the fact that it is for the best that there be one.) It does not seem any more problematic to posit such a fundamental principle as not needing further explanation than it is to posit the dynamical laws as not needing further explanation.
(Of course, some of us think there is a need to explain the dynamical laws. 🙂 And it counts in favor of 1a that a parallel putative explanation could be given for dynamical laws.)
hi Alexander,
Thanks for the comment. I have a few remarks but the issues involved will hardly be closed. First, I don’t think that claiming that 1 is false need “beg the question.” It depends on exactly what the design explanation is. There may be plenty of reasons to think some design explanations are false. For example, the design stories in Genesis, Hesiod, the myth of Pan-gu, as charming as some of these may be, are certainly false as literal accounts of the origin of our universe. I doubt you would disagree. The problem, at least for me, with the claim “There is a necessarily existent being who has the power to create any coherent physical configuration the being wishes, and who is motivated to create a configuration S in proportion to the objective value of creating S, and this being created a universe in the BB state because of the objective value of a universe starting in the BB state.” is that it is not a scientific hypothesis at all. Some would say that its not even false. Unlike the Maxwell’s equations, the theory of natural selection, or the cold dark matter hypothesis and so on… it has no further consequences that can be tested and doesn’t connect up with the rest of science. Some multiverse hypotheses also don’t have further observational consequence (some do) but they fit in with other parts of physics e.g. accounts of inflation in a way that the design hypothesis doesn’t. Even in my more sympathetic moments I have no idea how to evaluate your proposed explanation. If “value” means anything like it normally means I just don’t get the claim that the BB state has “objective value’ (what is the word “objective” doing here other than to weasel out of the observation that there doesn’t seem to be any value at all in a very hot and low entropy universe.) Has the universe increased (decreased) in objective value over time. does a de Sitter universe have a lot (little) objective value? Is there more of objective value on Mars than on the Earth? And is it really clear to you what a necessary being is, or in what sense it has wishes at all, or what the mechanism by which it acts on a wish and it explains why the universe started in the BB state? Is the relationship between its wish and the BB state causal? if not what is it? Knowing that you are a smart guy you may well have answers to these questions. But I am not sure that this particular discussion can be fruitfully pursued here since although issues in philosophy of religion touch on cosmology there are plenty of places to discuss philosophy of religion. So if you reply to my remarks that would be fine but I won’t continue the discuss here (though might via email).
The claim I was responding to was that 1 probably isn’t an explanation. I certainly do agree that it isn’t a scientific explanation.
As for value, that would require more discussion than we want to do here. I am inclined to think there is an aesthetic value in low-entropy states as such, but I was thinking not so much of the intrinsic value of the initial state, as of the value of having a universe with a clearly observable entropic arrow of time, with an interesting evolutionary history, etc. Of course, one can come up with scenarios where you have these things without a low-entropy initial state, say because you’ve got a downward fluctuation from equilibrium. But that sudden downward fluctuation would likely require either an extra miracle or for the universe to have sat near equilibrium for a very long time doing nothing very interesting, except maybe producing Boltzmann brains (which is another value-based count against it). This is not much worked out. But I have no good argument against the claim that such a value-based story could be worked out.
Let me first say that I’m in complete agreement with Alex Pruss. We should not dismiss (1) so quickly, and I think I have a reason for why options akin to (1) (i.e., those options which actually seek to explain the initial low entropy state of the BB) are in one sense better than option (4) (Barry’s favored view/position). Pace Barry, this reason seems to also suggest that the initial low entropy state of the cosmos does in fact cry out for an explanation.
Consider the following proposition:
(C): For any purely contingent proposition p, if p, then possibly it is explained that p.
Let a purely contingent proposition be a contingently true proposition that reports the obtaining of a purely contingent states of affairs (states of affairs which feature (solely) substrates or individuals that could have failed to obtain). Well, via reasoning agnate to Church (2009), Fitch (1963), Oppy (2000: 347-348 with some credit to Lloyd Humberstone for pointing out the similarity of his cogitation to Fitch (1963)), and Williamson (2000: 283-285, cf. 318-319) one can easily derive from (1) the following:
(R): For any purely contingent proposition p, if p, then it is explained that p.
assuming that the affix “it is explained that…” can be treated as a factive sentential operator (you don’t even need the additional posit that “it is explained that…” distributes over conjunctions). Well, explanation is certainly factive, so if you go in for (C) above, you’re stuck with (R).
Though the following requires further elaboration, I think you should believe (C) on the basis of strong inductive evidence from the sciences, and specific evidence from the fruit of the Reeh-Schlieder theorem in relativistic QFT (for some discussions of the fruit I have in mind see Redhead (1995a, b), Ruetsche (2011: 113-114), and Summers (2012: 7). I’m not suggesting that these sources agree with my connecting the fruit of that theorem to support for (C) above). In addition, I think that one’s belief that (C) holds can enjoy at least prima facie epistemic justification on the truth of the modal epistemologies of either David Chalmers (2002), H. Geirsson (2005), Dominic Gregory (2004), C.S. Jenkins (2010), or Stephen Yablo (1993).
Insofar as the initial BB low entropy state can have an explanation, it does in fact have one. Options like (1), which attempt to provide such an explanation, have a check in the “plus-column” over against options like (4) which involve a refusal to provide an appropriate explanans.
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For Works Cited see this link.
Hi Chris,
Thanks for your comment. I didn’t explain why I think 4 is promising but will in a later entry. It is a long story and involves particular views about laws, explanation and modality. I think the designer hypothesis is not a scientific explanation (a point with which [Alex Pruss and I] agree, and I should have said this in the first place) and there is room for argument whether it is an explanation at all. Perhaps that can also be discussed later. For now while I don’t want to get into a detailed discussion of your argument from (C) to (R) I will say that it seems to prove too much. Here is why. It is conceivable that there is a world w in which e occurs and is explained by laws and another world w* in which e occurs in which the laws are different and don’t cover e or even in which there are no laws at all. (both non-Humeans and Humeans about laws can agree with this) If explanation of contingent events requires subsumption under laws then e is an unexplained event in w*. So it is conceivable that there occur unexplained events. By the accounts of modality you refer to this is reason to hold that it is possible for there to be unexplained events. At the very least this shows that your argument makes some (controversial) assumptions about explanation.
Yes. Proper scientific explanans may necessarily require the ingredient “subsumption under” natural “laws” (borrowing your language). Assume they necessarily require such subsumption. If the actual natural laws were exhausted by a list L1, and some metaphysically possible world considered as counterfactual (call it W) did not include L1, but instead lacked natural nomicity altogether, then the occurrence of some event E1 at W would lack a scientific explanation (this is your point). This holds so long as the galaxy of metaphysically possible worlds extends beyond the galaxy of naturally possible worlds, and at least one member of the galaxy of metaphysically possible worlds lacks natural nomicity and yet features E1 [1].
My argument above was not restricted to scientific explanation solely. My cogitation allows for there to be an explanans of the initial low entropy state of the BB along the lines of the other modes of explanation (e.g., mathematical [2], grounding [3], metaphysical realization [4], causal [5], supervenience [6], and personal [7] explanation). That E1 lacks a scientific explanation does not imply that E1 lacks an explanation altogether. So hypotheses like (1) still out perform (4) in the sense that they at least attempt to provide the explanation the relevant state cries out for. And I think I’ve shown that that state does in fact cry out for an explanation.
Second, my argument’s domain could be restricted to states akin to the one with which we are concerned (i.e., the initial low entropy state of the BB…label states like this E2). We could also restrict the kind of explanation in view to scientific explanation. Our conclusion will now suggest (R*): For any E2, if E2 occurs, then E2 has a scientific explanation. The forgoing conclusion would follow from the mere fact that E2 could be scientifically explained. D.h., it would follow from (C*): For any E2, if E2 occurs, then possibly E2 is scientifically explained. If we assume (as you did) that something like the modal epistemology of Stephen Yablo (1993) holds, then the counter that it is conceivable that E2 occurs at a world W, and so could be scientifically brute, falls short of a successful criticism of my reasoning.
On Yablo’s account (1993: 34-35 but I’m quoting my own summary of him elsewhere [8]), “if some proposition r is thought to be conceivable, and there’s another proposition s which materially implies the necessary falsehood of r, and regarding r as conceivable ‘is explained by…[one’s] denial'” [8] (Ibid., 34) or unawareness (Ibid., 35) “that s and/or [one’s] denial or unawareness that s materially implies the impossibility of r, and s does in fact hold, then [one] has a defeater for [one’s] belief that r is metaphysically possible.” [8]
Now let s be the proposition that possibly, Sean Carroll’s multiverse explanation [9] (or any other suitably similar competing scientific explanans) of E2 holds. And let r be the proposition that E2 occurs at W and is scientifically brute. Given our assumptions, it’s clear that your conceiving that r is explained by either your unawareness or denial that s, your unawareness that s materially implies the impossibility of r, or simply by your denial that s materially implies the impossibility of r. But clearly, s does materially imply the impossibility of r, and by our lights, s. So you have a defeater for your belief that r.
Notice that my argumentation sets down upon you the burden of showing that E2 isn’t contingently scientifically brute, but necessarily scientifically brute. That is to say, you’ve got to show that competing scientific explanans are not even possible. That’s a crippling burden for anyone not keen on invoking the limits of scientific explanation.
For notes and references see this link here.
I want to suggest a fifth way of looking at Penrose’s problem, though in someways it overlaps with the statements of both (3) and (4).
(5) One could hold both that something was inexplicable with respect to an existing scientific framework, construed very broadly; and that a later framework might be expected to explain it. That there are such facts at any time seems unavoidable, because any framework has to assume something — yet later, broader assumptions can explain the earlier narrower ones.
I distinguish (5) from (3), as stated, in degree of shift between frameworks — I have in mind something more than ‘tweaking’ the dynamics, even to allow universe generation.
I think a (semi-)historical analogy may help: the question of why the sun and not the earth is at rest, between Copernicus and Newton. Whether this was true was an open(ish) question, and some of the debate could be construed as over whether a stationary sun could be explained — e.g., Kepler’s religious ideas. But ultimately, in the Copernican framework there is no proper explanation. Now consider Newton’s theory: first, one would not get close to universal gravitation just by looking for an explanation of the sun’s rest — Newton needed detailed mechanical and astronomical data. The rest of sun (‘in the frame of the fixed stars’, not in some absolute Copernican sense) is only a small part of that.
Second, it’s not actually true that the sun is at rest (even granted N’s assumption that the center of mass of the solar system is at rest). Third, while the approximate rest of the sun is explained in the CMS frame of the solar system, that precise notion of motion is just not available in the Copernican system, so the explanans changes profoundly with the theory. So in fact, the explanation of the sun’s rest played a much more important role in illuminating the novel foundations of Newton’s theory (the inertial/accelerated motion distinction), than in discovering it.
My observations are not terribly original, but illuminate a couple of points relevant to this discussion. (I think the observations generalize: much the same could be said about the question why space is Euclidean in the development of relativity, though perhaps Einstein’s use of the Newtonian principle of equivalence is a counter-example.)
To think that anything — however fundamental it seems — is forever beyond explanation is an exercise in hubris. Still, I have sympathies for (4), if it is understood as saying that within our current framework, initial low entropy is just a given.
Historically, fundamental assumptions are not very useful data points; experience suggests that physics won’t get very far just by attempting to explain low entropy. On the other hand, attempting to explain it with empirically driven, developing theories/theory fragments could be a very useful exercise in understanding their foundations — and hence in their further articulation. Indeed, the deep reason that I want to distinguish (5) from (3) is to highlight the way in which basic assumptions in an existing theory assist in finding a new one.
(5) is an alternative to (1).
Your suggestion of a fifth way of looking at Penrose’s problem is very compelling. The solution of this and of many of the other 13 questions raised for this blog could well benefit from a change in scientific framework. Penrose himself suggests an approach using twistor theory as a relativistic scheme in which the twistor objects are the carriers of quantum entanglement. “Ordinary space-time notions are not initially among the ingredients of twister theory but are to be constructed from them.” Abandonment of the primacy of spatial and temporal relations between events opens up new avenues of addressing the 13 questions at issue here and this, as well as other possible framework suggestions, should be considered an acceptable mode of discussion in the present blog.
Nick I am in semi-agreement with your position. As I suggested in an earlier comment (which apparently failed to pass moderation??) that I believe in a multiverse where something like cosmic natural selection (such as that proposed by Lee Smolin) can provide a causal mechanism which provides a scientific and quantifiable explanation for why our universe has the characteristics it currently does. I do not feel an external designer is a requirement for expanation. This is admittedly a radical and unorthodox approach but in my opinion one worthy of consideration. It is certainly less radical than the idea that there are external forces at work.
e.
Barry,
Your first question asks whether the entropy condition of the universe at the Big Bang “requires explanation.” In general, how does a philosopher approach the problem of discerning which phenomena “require explanation” and which do not?
Allan,
I can’t answer “how does a philosopher approach…..” since different philosophers have various views about what explanations are and what phenomena are basic and not further explainable and what phenomena are especially in need of explanation. I had in mind the view that the very low entropy state at the time of the early universe cries out for explanation since it is so “unlikely.” But there is a question, one that philosophers as well as others have thought about, concerning what “unlikely” means in this context.
Well, first, in the interests of full disclosure, I think every contingent proposition calls out for and has an explanation, and I defend this in my PSR book. But even if this controversial thesis were true, I think we’d feel that the initial low-entropy state somehow “especially” calls out for explanation.
In any case, it isn’t just unlikeliness that makes the state seem to call out, or especially call out, for explanation. For any initial state of the universe, there is some entropy-based description under which it is unlikely. Suppose the universe started with entropy e0. Let epsilon be some very, very tiny number. We can now ask: “Why did the universe start with entropy between e0 – epsilon and e0 + epsilon?” And if we choose epsilon small enough, the universe’s so doing will be just as unlikely as the Penrose 10^(-10^123), even if e0 is very close to equilibrium. But the starting entropy being between e0 – epsilon and e0 + epsilon doesn’t seem to especially call out for explanation if e0 is very close to equilibrium, in the way the low entropy state seems to.
Maybe what makes us feel that the low entropy state especially calls out for explanation is a combination of two things: (a) unlikeliness and (b) significance. The significance can be explanatory (e.g., the state explains a lot about the subsequent evolution of the universe) or axiological (the state makes possible a particularly valuable kind of universe) or both. When something very unlikely happens and it’s significant, we feel like an explanation is especially called for. I think we’re right to feel this, but one can accept this story even if one doesn’t accept that the feeling is appropriate.
Thanks, Barry. I guess at least we’ve established that the high entropy state of the philosphy of science requires explanation.
With regards to Barry Loewer’s fourth suggestion (taken to mean that a better explanation of the basic dynamical laws might eventually lead to an explanation of the BB state) and the debate over whether PH “cries out” for an explanation, I think it’s relevant to begin with the five main problems which are directly related to the highly successful standard empirical model (GRT+RW):
i. A Newtonian absolute time (Weyl’s principle: causal coherence of the bundle of fundamental worldlines) needs to be assumed, even though relativity theory is supposed to reject that in principle.
ii. The principal cause of expansion is a singularity—so the theory gives no prior explanation for expansion.
iii. The large-scale isotropy indicates that there may be no causal horizon.
iv. The measured expansion rate indicates that the emergent 3D universe:
a. is flat, which is statistically impossible; and
b. contains mostly (~96%) cold dark matter and dark energy (cosmological constant).
(iii. and iv.a. are supposed to be resolved by inflation; however, a very readable critique by Steinhardt in Scientific American’s April 2011 issue raises doubt about the theory’s actual effectiveness in doing that).
Now, the connection between i. and the entropic arrow of time may be essential or accidental. PH proposes that the entropic arrow of time is fundamental, or is essentially linked to some fundamental aspect of the Universe. If so, the “extraordinarily special” initial state would really “cry out” for an explanation. But if i. were truly fundamental, the fact that the Universe’s entropy can never decrease could be due to an accident of the fundamental dynamical laws, so that if those were to be worked out the entropic arrow and the “unlikely” BB state might eventually be explained as a result.
Personally, I think i. needs to be addressed more directly, as it may well be related to those fundamental dynamical laws. SRT, as a special case of the standard model, proves very illustrative in that regard: as a 3D universe, given by prior definition, evolves, it is synchronous only in the cosmic rest-frame. In the proper frame of any observer in uniform absolute motion, the universe evolves equably, but at an angle from the synchronous spacetime hyperplane. Two such observers could therefore always synchronise clocks in the usual way, but that would be artificial because simultaneous phenomena for them would not be simultaneous noumena; the arrows of “manifest” and “production” time would be mis-aligned (see, e.g., Callender’s talk at youtube.com/user/FQXi for some surrounding discussion).
The fact that this can be done in SRT is important because, along with causal coherence (which means that every single event in the bundle of fundamental worldlines is associated with a well-defined 3D set of others with which it “really” occurs simultaneously, regardless of perceptions in a relatively moving frame), the RW line-element also assumes hypersurface orthogonality to the worldlines in the cosmic rest-frame (see, e.g., arxiv.org/abs/1006.5848). But how should these assumptions really be justified in general? and why should the latter be needed anyhow, when an absolute cosmic time has already been assumed? For instance, what if the fundamental worldlines corresponding to Weyl’s “average rest-frame” are not geodesics?
I think this line of inquiry falls right in line with investigating the basic dynamical laws (principles, axioms, assumptions of the theory) analytically, as a means of potentially resolving the problem of the BB state.
Just to qualify i.:
“Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time”.
Although a neutrino, created in a star 13 billion years ago, will have been travelling through the Universe near to the speed of light, so that its proper time “now” may be only 20 minutes, say, cosmology still maintains that it has “truly” existed for 13 billion years, in the Universe which has never been synchronous in its proper coordinate system. Similarly, in observing the dipole anisotropy in the CMB, we infer that it is due to our motion with respect to the cosmic rest-frame. Therefore, one of the basic assumptions of cosmology is inconsistent with the notion in relativity theory, that there can be no privileged observers. If the former should need to be maintained in order to properly describe our actual Universe, it may indicate a dynamical law to which any meaningful relativistic description should have to ultimately remain consistent.
The physical laws of our universe, together with its initial low-entropy state, may be *more* probable than a universe with different physical laws but a higher-entropy initial state.
To Alexander Pruss (above: the comment thread is too narrow):
Feynmann, following Boltzmann, is considering two hypothesis:
Non-Fluct: hypotheses that the low-entropy initial state of our epoch did not arise via a fluctuation from any earlier state of equilibrium and
Fluct: hypothesis that it did arise via such a fluctuation. Note that these hypotheses do not specify exactly what the local entropy minimum, going backward in time from us, is. It may or may not be a state similar to that postulated in standard cosmology.
Feymann’s claim is that Fluct makes specific predictions, if we conditionalize on all present information we have (which does not include the exact form of the local entropy minimum), namely that new data should reveal equilibrium in new places. Non-Fluct does not in any obvious way make any such prediction (one would have to fill in some details here to make Non-Fluct more exact). Is there any disagreement yet?
If so, continuing observations disconfirm Fluct.
If I am following, you seem to want yet a third hypothesis, which combines whatever low-entropy state Non-Fluct settles on with the additional stipulation that that state arose via a fluctuation. But the third hypothesis does not change the situation. Fluct, as it is, assigns a tremendously small probability to continuing observations that do not reveal equilibrium. Those tremendously small probabilities will just be converted to the same tremendously small prior probabilities of your third hypothesis, conditional on all information we have. Since the third hypothesis postulates that the local low-emtropy state arose via a fluctuation, one must take account of the probability that the theory assigns to such an event by the theory.
Stupid question: how does quantum uncertainty or fluctuation apply at the original bb singularity, given that the quantum of action is so exceedingly small and the energies contemplated at the bb event is maximally large, ie. “contains all the energy in the universe”?
Apologies: I hadn’t read this thread until just now, so am commenting a little late, but I thought it might be worth drawing people’s attention to a very different kind of response to Penrose than those mentioned above; namely that of mathematician Ian Stewart. When I interviewed him in 2008 about (inter alia) fine-tuning, I mentioned Penrose’s argument:
“While, as you point out, several physicists and cosmologists have begun to explore what happens when one varies several constants at a time, and have indeed concluded that the probability of the existence of (e.g.) stellar structures may not be as low as first thought, such models are still based on the same low-entropy initial conditions of ‘our’ Big Bang, which have been shown, by Roger Penrose among others, to be stupendously improbable themselves (estimated by Penrose to be of the order of about one part in 10^10^123, a number which surely cries out for explanation).”
His response was as follows:
“[…] Penrose’s calculation is absurd. It assumes a purely thermodynamic universe. Here all forces are short-range – acting only at the level of collisions of molecules – and repelling. The result is a long-term trend towards a uniform distribution of matter (disorder). But the real universe has many other forces, notably gravity. This is long-range and attracting – the exact opposite. The result is a long-term trend towards ‘ordered’, clumpy distributions of matter. If you use a thermodynamic model on a gravitic system, the results won’t make much sense. I don’t actually think the use of ‘order’ and ‘disorder’ when discussing entropy is very helpful, because those terms are highly ambiguous, but for the sake of simplicity let’s say that a high-entropy state is disordered and a low-entropy state is ordered. Then thermodynamic effects turn order into disorder; gravitic ones do the reverse. So any natural ‘final’ state of a gravitic universe is highly ordered. If you now pretend it’s a thermodynamic system, the initial state must have been even more ordered (because entropy increases over time). This leads to Penrose’s minuscule estimate for the probability of the presumed initial state that would lead (by thermodynamic action) to the final one. However, that’s not how it happens. Instead, an initially disordered state naturally clumps under gravity. ‘Entropy’ measured by the clumping decreases over time. It doesn’t increase.”
Stewart has made this argument at length in a paper that can be found at the link below:
http://109-231-69-82.flexiscale.com/OUP/0195150708.Oxford.University.Press.USA.From.Complexity.to.Life.On.The.Emergence.of.Life.and.Meaning.Nov.2002.pdf#page=119
I’d be very interested to hear what people think about this response, should anyone care to comment.
I believe that Stewart is correct. Consider that the important source of low entropy on Earth today is the Sun, which attained its initial low-entropy state through gravitational action, not as a byproduct of a Big Bang low entropy state. One can imagine a universe starting in an extended spatially random (i.e., Poisson distributed) state of baryonic and “dark” matter. It could then subsequently evolve to form low-entropy structures such as stars, galaxies, clusters, etc., purely through gravitational action. The source of low-entropy in this case would clearly be gravitational, and certainly not the original extended random spatial distribution. But, it is difficult to see a significant difference between that case and that of the universe produced by the assumed Big Bang, which is also considered to be initially in a compact, but otherwise random state that expands to eventually produce a larger random spatial distribution of baryonic and “dark” matter that then gravitates. The only way that the initial Big Bang can be considered to represent low entropy is by virtue of its spatially compact state, relative to more extended states that it might have had instead. But this assumed compact state represents the entire universe at that time. There is no other extended space for it to occupy. So its compact state has no bearing on its entropy. In summary, it appears that it is gravitation, not the Big Bang, that is the source of low entropy in our universe.
Many thanks for your response, Gary. I too find this argument quite compelling, but as with so-called “fine-tuning” (against which there are also very simple and prima facie devastating arguments) I hesitate to conclude this is the end of the story simply because there are so many scientific and philosophical luminaries who keep on telling us that there is something truly astonishing — something that cries out for a very special kind of explanation — involved.
It would be great to get comments from others. I think Stewart’s argument (and that of Gary above) are at the very least worth considering, no?
I disagree with Stewart’s assessment of gravitational entropy, as I consider Penrose’s description more reasonable and consistent with the relevant physics. From a gravitational perspective, since gravity causes matter to tend to clump, a uniform distribution should be considered highly ordered. Therefore, as gravitational systems do naturally tend to cluster over time, the disorder or entropy should increase in accordance with the second law. In section 27.10 of The Road to Reality, for example, Penrose points out that this is consistent with the Bekenstein-Hawking equation for entropy, which describes an inverse relationship between entropy and surface area; thus, the entropy of a one solar mass black hole is greater than that of the Sun.
Furthermore, Stewart’s position seems untenable from a cosmological perspective: if entropy naturally tended to decrease in gravitating systems and the Universe began in thermal equilibrium at a hot Big Bang, there seems little hope for the overall entropy of the Universe to be reconciled with the second law. In contrast, as Penrose concluded in section 27.13 of the same book, ‘Gravity seems to have a very special status, different from that of any other field. Rather than sharing in the thermalization that, in the early universe, applies to all other fields, gravity remained aloof, its degrees of freedom lying in wait, so that the second law would come into play as these degrees of freedom begin to become taken up. Not only does this give us a Second Law, but it gives us one in the particular form that we observe in Nature. Gravity just seems to have been different!’ Thus, Penrose reconciles observation with the second law by arguing that the overall increase in gravitational entropy over time would overwhelm the overall decrease in the thermal entropy of the Universe.
Basically, while both Penrose and Stewart recognise that there is a stark contrast between gravitational and thermal entropy, I think Penrose is correct in his assessment that while entropy should naturally tend to increase in both systems, in the case of gravity this should occur as matter clusters together; whereas I think Stewart’s position—that in both cases clumpiness signifies order and uniformity the opposite, so that gravitational entropy should naturally tend to decrease—is likely incorrect.
Many thanks Daryl — this is really interesting and helpful. I’ll have to go back to Penrose’s RR and chew it over some more…
The entropy of a system is a function of the probability distribution of its available dynamic states, and does not generally follow simply from a description of the forces involved in the system dynamics. Thus, asserting that since “gravitational systems do naturally tend to cluster over time, the disorder or entropy should increase” would not be an acceptable way to characterize the change in entropy of a system. Furthermore, a “uniform distribution” of matter generally refers to a Poisson spatial probability distribution of the particles, and does not imply that the particles are uniformly spaced. The latter would indeed define a very low entropy system, but the former is characteristic of a system in equilibrium, which is a state of maximum entropy. A clumping of the particles due to gravity (ignoring other effects) can only reduce the entropy of the system.
As for Penrose 27.10, the discussion there applies only to black holes, so the relevance to the present discussion is far from clear. And in 27.13, Penrose makes the assertion of specialness regarding the Big Bang that is the subject of discussion here, so appealing to this reference is begging the question. In any case, in the quote you cite, it is not clear that Penrose is claiming that gravitation increases the entropy of the universe. His discussion would instead seem to argue that gravitation comes into play late enough in the evolution of the universe so that other effects that increase entropy dominate, and the overall entropy of the universe still increases in accordance with the second law.
Gary:
In physical cosmology, a ‘uniform distribution’ of matter refers to its description as an isotropic and homogeneous perfect fluid, which, although there has since been localised clustering, remains a fairly valid large-scale description, as evidenced through the success of the standard empirical theory that models it as such. The standard interpretation of the CMB, however, is that at decoupling all the matter in our current observable universe was in a thermal state, so that this uniformity should have existed at all scales. Gravitationally speaking, this was an unstable critical point, so that small deviations from perfect uniformity at the time of decoupling led to local collapse throughout (standard theory of galaxy formation). Thus, the Universe will only reach gravitational equilibrium in the final stage of each cluster’s collapse.
There are multiple issues with your second paragraph, and I’ll try to address them as concisely as possible, by referring to sentence numbers. (1) As you are propounding the exact opposite as Penrose, discussion of the inference he draws from 27.10—that the physical distribution of matter in gravitational equilibrium is exactly the opposite of the distribution of matter in thermal equilibrium, so that a clumping of particles due to gravity does in fact *increase* gravitational entropy, with its maximum therefore reached when all particles in a box collapse to a point—is therefore entirely relevant here. And since this point is crucial to the main argument in 27.13, it must be correctly understood if you care to understand Penrose’s eventual point, even if for the purpose of subsequently presenting a coherent argument against it. (2) I didn’t appeal to this reference for my own purposes and thus ‘beg the question’, but only attempted to explain what Penrose’s point there is, as I think it has been misunderstood here. There was not an original thought in my post, unless that arose from my own possible misunderstanding of his point:—that despite the fact that the Universe began in a thermal state, its total entropy was initially extraordinarily less than what it might have been *because* the gravitational entropy of that state is minimal—and the entropy per baryon in gravitational equilibrium (black holes) completely dwarfs the value when those baryons are in thermal equilibrium. (3) You’re insinuating that I’ve quoted Penrose out of context. If I have misunderstood Penrose and thus misrepresented his meaning, by all means criticise; but in general, an argument that a brief quotation may be interpreted differently than it has been presented is very weak in that respect. In any case, the fact that ‘Penrose is claiming that gravitation increases the entropy of the universe’ is actually the whole point of 27.13 (and the discussion leading up to it). (4) Dead wrong—please read those few pages carefully and see for yourself.
Rereading my last and previous comment in this blog, it occurs to me that one might conclude that I am asserting that gravitation somehow subverts the second law of thermodynamics. Let me assure you that I firmly believe in the validity of that law. The need for brevity in the blog format can encourage oversimplification and lead at times to possible misunderstanding. The parenthetical phrase “ignoring other effects” in my last reply was the replacement for a long paragraph about the additional effects of gravitation in raising average particle velocity and system temperature, which tend to increase entropy. My point was that the matter clustering effect of gravity taken by itself, by reducing the volume of the material, is entropy reducing. (If temperature were kept constant through heat radiation, which is of course not consistent with system isolation, the entropy of the remaining clustered system would indeed decrease.) The direct effects of gravitation, including star and planet formation, are clearly essential to the emergence of life in the universe, and would not occur if not for gravitation. And even the side effects of this gravitation, though entropy increasing, ultimately result for example in the nuclear processes that produce potentially life-supporting energy radiation from stars. It is in this spirit that I emphasize the importance of gravitation and its entropy reducing effects. The independence of these benefits from any “special” low-entropy condition of the Big Bang is worthwhile contemplating. The subject of this Big Bang “specialness” itself is another matter, and is much too complex for me to attempt to discuss further here.
“My point was that the matter clustering effect of gravity taken by itself, by reducing the volume of the material, is entropy reducing. (If temperature were kept constant through heat radiation, which is of course not consistent with system isolation, the entropy of the remaining clustered system would indeed decrease.)”
This is the crucial point in your contention with Penrose. While you are arguing that the arrow of gravitational entropy points in the same direction as its thermal counterpart, he argues that it points in the opposite direction—and with a greater magnitude that eventually leads to the one part in 10^10^123 estimate.
Daryl,
I don’t see how one can debate my last assertion regarding the decrease of entropy in a gravitating cloud of matter at constant temperature, which follows directly from a standard equation of thermodynamics. Of course, if the gravitation eventually results in the formation of a black hole, things change drastically in that process. All of the precious statistical information that has accumulated during the earlier clustering is lost as the matter enters the event horizon, resulting in a huge increase in entropy. I don’t doubt that conclusion, but wasn’t carrying my considerations to that extreme. But still, I find your points very interesting. Penrose’s arguments for BB specialness are not easy to dispute, but I believe that they will ultimately prove to be far less mysterious when the process of universe formation is better understood.