Daniel Holz writes on a popular science blog Cosmic Variance:"The Copernican principle is a guiding foundation of cosmology. In short, it states that we are not in a privileged place in the Universe. A “random” observer will see the same Universe that we do." He further writes "Now suppose I told you I had a model which explained all of the observations, was based on general relativity, and appealed to no mysterious dark energy component... There’s one important caveat, however. The void model throws out the homogeneity and isotropy assumption. The Universe is now spherically symmetric, with a big hole in the middle. Even worse, we happen to be very, very close to the center of the hole."

Let's suspend discussion of what is more "plausible", dark energy or giant void, or what "plausible" even means as applied to the 'universe as a whole', or what justifications one might offer for the Copernican principle. There seems to be an overt non-sequitur in its application. Assuming that we are not in a privileged position does not imply that we are in a generic one. The third option, and seemingly the most "plausible" one, whatever that means, seems to be that our position is neither privileged nor generic. There are many like it, and there are many as well, that are nothing like it.

But much of Big Bang cosmology is based on extrapolating what we observe to the entire universe, in other words it is based not on the Copernican principle, but on its non-sequitur. The whole reasoning is uncomfortably reminiscent of Kant's antinomy of space and time, where one gets a contradiction by applying forms of experience to categories that go beyond any possible experience, such as 'universe as a whole'. Similar reasoning is also used when talking about the "wave function of the universe".

Is the philosophical status of Big Bang cosmology epistemologically different from that of most scientific theories in that it explicitly relies on metaphysical principles and reasoning? Is the argument from the Copernican principle salvageable at least as a hypothetical, or is it just a misapplication of concepts?

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    I don't think "in the middle" of the universe is physically meaningful. I don't understand what you mean by "its non-sequitur"; could you make it clearer? [edited out some bits ... (deleted ensuing comment war)] – Cheers and hth. - Alf May 24 '15 at 5:28
  • 1) "In the middle" can mean just "at no edge", there is a hole in the middle of most donuts, but it can pretty much be anywhere in the donut, given that a torus is without edges. 2) The non-sequitur is the one pointed out in the prior paragraph: deducing from the fact that we are not in any 'special' location the idea that everything must be very much like it is here. (Using 'its' with 'non-sequitur' is notably jarring, so I get how this reads as meaningless.) – user9166 May 25 '15 at 14:50
  • I believe it is the current view that, depending on what model of inflation one chooses, homogeneity and isotropy may not be universal principles, although they certainly appear to apply in the observable universe. Also, I don't think it entirely fair to say that cosmology explicitly makes assumptions of a metaphysical nature. There is a hard science part of cosmology which makes predictions of a metaphysical nature. But this is also true of quantum theory. Clearly cosmologists are more inclined to explore these predictions because their theory is relatively meagre. – Nick May 25 '15 at 18:08
  • @Cheers and hth. - Alf "In the middle" is meaningful if the model assumes spherically symmetric universe with a center, as the void model does, see links. "Non-sequitur" refers to "every place is generic" which is a non-consequence of the Copernican principle, asserting that Earth is not special. I added a link on Kant's antinomies that provide some context for the phrasing of the question, the point is that applying empirical generalizations to 'universe as a whole', 'first cause', etc. is misguided. Hope that clears it up. – Conifold May 26 '15 at 21:05
  • @Cheers and hth. - Alf You misunderstand Baez. There is no center in the Big Bang model that he describes, or other models that take spatial sections of spacetime to be 3-spheres. However, this is assumed, not observed, there is no sound way to infer global geometry of space from local empirical observations like ours. Void models simply assume a different geometry, where there is a center and a periphery. By the way, Baez is not a cosmologist unlike Holz, he is a mathematician. – Conifold May 26 '15 at 21:48

I think 'non-sequitur' is a vast overstatement, and this is a mere 'over-generalization'. And not even very far 'over': the statement cannot generalize absolutely, but it does generalize pretty well.

In a strong sense the homogeneity assumption is itself an application of the Copernican Principle. It is the assumption that we do not happen to inhabit a place where space is especially 'nice', in the sense of having the "Goldilocks" quantity of matter: that we don't live somewhere too special.

So this is just a disagreement as to what flavor of 'general' is most objective, and either side relies upon a strong injection of the 'Copernican' ideal, but in different forms.

Unwinding your objection to the Big Bang theory -- the weakest point is that it assumes that time is uniform in a very strong sense. It gets into big trouble if you follow the history of expansion back to when space would have to move objects apart faster than the speed of light in order to expand quickly enough. So, you can toss out the uniformity of time, but then the rationale behind continuously extrapolationing time back across trillions of years gets a little questionable. Why shouldn't time have changed again and again?

The notion of the field particles arising out of the Higgs boson early in the history of the universe "when the rules were different" is the same sort of thing, it puts the irregularities away from us, so we feel like that place is special, not ours. Why assume the rules got decided at a given energy level and then stuck there forever? Why should they not slowly adapt across time? (And if we don't get to be special, why does anyone else? Harumph, <pout/>.)

We end up with the notion that time and other basic forces can be significantly different, but in general they are just like we see them where we live. In the same way the homogeneity of density is Copernican, so is this notion of time and fields. It is about the familiar being general so that we don't imagine we are special again.

I don't see the disconnection needed to make this a non-sequitur. The Copernican Principle is properly applied here, and if anything, too healthy. (From a Nietzsche angle, in rejecting the deductions of our slave-morality religion: that we are all equally special and masters are evil cheaters; we have taken up an even more slave-morality position on specialness: that we are not worthy -- we do not deserve it, but someone must.)

The principle is internally inconsistent as a metaphysical principle: not all notions of 'general' can be equally objective, because we are someplace, and that place really will have some idiosyncratic properties. And picking and choosing which ones are most objective, just to favor the chosen explanations of our own physics, would violate the principle itself. Our place would be special in that it allowed us to truly see what was and was not special about it from experimental data.

But that does not undermine its usability as a component of theories. It just requires compromise between different applications of the principle to be chosen by each theory. We just have to guess what is and is not special about home until we get a good sense of life abroad.

---- Separate second answer:

There is also a compromise to be struck between the Copernican principle and the (Weak) Anthropic one. It is not impossible that things work out the way they are because we are here to observe them. A lot of biologists think we are in the "Goldilocks zone" of energy balance, and life is much less likely to arise at any other point on the spectrum of energy balance because small polar molecules in liquid form are scarce. And we do not accuse them of being anti-Copernican, we let this idea guide where we are spending public money looking for planets with life.

We could also be in the "Goldilocks zone" of matter distribution, where observers are unlikely to survive elsewhere. The odds of just one hole goes down, but the theory of massive variations in distribution itself could still make sense.

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  • I don't think it is an overstatement, it literally "does not follow". Big Bang assumes that not only time but space is strongly uniform, which is a quantum leap from Earth is not special. Recall how Aristotle took the known part of the solar system, encased it into a crystal sphere with fixed stars pinned to it, and called it Cosmos. Big Bang cosmology in popular presentations similarly takes the rules of the little neighborhood we happen to inhabit, and blows them up to the size of Cosmos. – Conifold May 26 '15 at 21:20
  • A more reasonable speculation is that universe has multiple patches of different character, and there is no "generic" at all, and therefore no "special". This is exactly the position taken in string theoretic braneworld cosmology, where we inhabit a (mem)brane in higher dimensional space, and Big Bang is caused by a collision of branes. The collision is a local event even on the brane, and only affects a small patch of it, it certainly has nothing to do with 'universe as a whole'. I am not saying this is more 'plausible', but it certainly is more 'Copernican'. – Conifold May 26 '15 at 21:25
  • There are no degrees, it seems. Once you have decided every overgeneralization is a non-sequitur, why try to argue any intermediate position at all? Obviously every minor flaw in logic is in some sense a non-sequitur, but it does not make fora reasonable way to find interpretations of things. – user9166 May 26 '15 at 23:30
  • I am equally suspicious of the Big Bang, but I don't think it requires us to generate a whole multidimensional space of crazy, inaccessible multiple universes. I am not sure such a response is scientific, or can ever be pulled back into any testable realm. It only requires looking more closely at the assumptions already made, not making tons more. – user9166 May 26 '15 at 23:33
  • I am on board with inductive generalizations, and pragmatic reasoning. But this particular gap does not seem minor to me, it is an equivalent of concluding that everything is white because existence of other colors would make white special. I also do not find braneworlds very attractive, my point only is that Big Bang is an extrapolation of very limited significance, far short of cosmic proportions. A storm in a teacup so to speak. – Conifold May 27 '15 at 0:37

The 'Copernican principle' wasn't a means by which Modern Science was constructed; if one takes account of its entire history; it's a summation of some general principles that have been discovered; there's a speculative character to Physics which isn't generally noted - though it should - when one gets beyond what can be directly tested for; the main metaphysical principle is Occams Razor in one of its many forms: here, physical laws that are known now are pushed back (Smolin for example suggested that it might be useful to explore if laws change in the distant past; though of course one can ask whether the laws that underlie this are immutable; but that would be a philosophic metaphysic; whereas Smolins is an actual move in the edifice of physics).

But the point of Big-Bang cosmology is that proceeds on a long-established science, much longer than physics itself: astronomy; I hadn't realised just how relatively recently it became consensual.

Interestingly, The Belgian priest Lemaitre who theorised it called it the 'primeval atom'; which is another sense of atom; it also, interestingly, tracks Hegels 'History of Philosophy'; where he drew out the phenomenal Democritean atoms from the immutable Parmenidian atom; according to this article - he was also interested in the philosophic issues it raised - which were many; but unfortunately it doesn't go into it.

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  • Its newness seems obvious in it being named after someone from the second millennium. Historically, Ptolemy is the basic cosmology in Europe, and it seems clearly more in the spirit of Occam's Razor to have one center of the universe. So throwing astrophysics back on traditional astronomy in the hope of making sense out of this seems counterproductive. – user9166 May 25 '15 at 17:16
  • I prefer to distinguish between metaphysical principles, that apply to reality, and methodological ones, that only apply to our theories of it. Elegance, consistency, Occam's razor are (or can be rephrased as) methodological, other things being equal a simpler theory with fewer entities is preferable on practical grounds. Copernican principle is a claim about reality rather than a theory of it, so on its face at least it is metaphysical. – Conifold May 26 '15 at 21:34
  • The aspect of Big-Bang cosmology that follows long-established science is that assuming our vicinity did not interact with external entities its recent history looks a certain way. This is a far cry however from popular dramatizations about the birth of the universe, etc. But the best part is that this modest version does not require any Copernican principle. – Conifold May 26 '15 at 21:38

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