A Bang into Nowhere: Comments on the Universe Expansion Theory
| Scientific Paper | |
|---|---|
| Title | A Bang into Nowhere: Comments on the Universe Expansion Theory |
| Read in full | Link to paper |
| Author(s) | Constantin Antonopoulos |
| Keywords | beginning of Time, the Universe, galaxies drift |
| Published | 2003 |
| Journal | Apeiron |
| Volume | 10 |
| Number | 1 |
| No. of pages | 29 |
| Pages | 40-68 |
Read the full paper here
Abstract
The notion of a first ever moment of Time is self-contradictory: In lacking a moment before it, it lacks a lower barrier, so there is no stopping it from — inconsistently — receding further and further into an infinitely remote past. Hence, there cannot be a beginning of Time. Only a beginning in Time. The notion of the expansion or growth of Space is incoherent. Objects growing in Space grow by taking up more of space. But for Space to do that, Space must take up more of space, and in order to do that Space must be larger than it is. Hence, there can be no expansion of Space. (Only one in space.) Furthermore, there is no such thing as "the Universe." "The Universe" denotes no special object; in fact, it denotes no object of any kind. The fact that all things have a cause does not mean that "the Universe" has a cause any more than the fact that all men have a mother means that Humanity has a mother. Hence "the Universe" does not have a cause. "The Universe" does not have an age. "The universe" is a short hand, comprehensive reference to all things that exist. And things being many, they have many ages. Hence, there is no such thing as the age of "the universe," unless we mean an ...average age. "The Universe" is just an inventory word, an inventory meant to be exhaustive. And inventories have no size. (I guess.) Hence, "the universe" has no size either. Universe expansion theorists mention an 'observation', documenting the fact that galaxies drift apart from one another, without however having moved an inch! "Only the space in-between them grows." This is the sort of empirical confirmation that a theory of the sort here criticized truly deserves.
Overview
Constantin Antonopoulos wrote this from the Division of Humanities at the National Technical University of Athens, and it is a philosopher's paper in the strict sense: it contains no equations, no data and no alternative cosmological model. It is an attack on the intelligibility of Big Bang cosmology conducted entirely by conceptual analysis. The claim is not that the expanding universe is unsupported by evidence but that its three central locutions — a first moment of time, the growth of space, and "the universe" as a thing with an age and a size — are self-contradictory, so that no evidence could support them, since there is nothing coherent for evidence to be evidence of.
The paper's diagnosis is that all three failures are instances of one mistake: applying to Space, Time and the totality of things the very predicates whose meaning presupposes those things. Antonopoulos calls this the fallacy of self-reference, and combines it with two fallacies he takes from a 1955 note by E. H. Hutten in the British Journal for the Philosophy of Science — reifying abstractions, and confusing the properties of a set with the properties of its members — arguing that in practice the three collapse into one. He treats the modern textbook formula that galaxies are stationary while the space between them grows as the reductio of the whole enterprise, and dubs it "the physics of ghosts". His allies in the text are Kant, Hutten, and the physicist Lewis Epstein; his named targets are Adolf Grünbaum, Edward Harrison, William Kaufmann, and Sten Odenwald and Richard Fienberg.
The argument
1. Why there can be no first moment of time
Antonopoulos begins from the ordinary reaction to any creation story — "yes, fine, but what was there before that?" — and argues that its persistence, despite cosmologists' insistence that the question is ill-formed, indicates something ineradicable in reasoning rather than mere naivety. He quotes Grünbaum's statement that in the Big Bang model "there were no such earlier instants before t = 0 and hence no instants when the big bang had not yet occurred", and objects first that Grünbaum shows no awareness of Kant's contrary thesis that time is a necessary representation which "cannot itself be removed" though we can think it devoid of phenomena.
His own argument is independent of Kant's authority and is the sharpest thing in the paper. Instants, he says, are relational entities: "before/after", "before/now" and "now/after" are mutually constraining pairs, like husband and wife, and "time is succession". A determinate moment t′ is determinate precisely because it sits between an earlier t1 and a later t2; the two neighbours are its upper and lower limits, and it is fixed in the series because both exist. Now consider t = 0. It has later neighbours, so it has an upper limit. But by stipulation nothing precedes it, so it has no lower limit — nothing earlier than which it cannot occur. Antonopoulos then performs the move the paper turns on: he shifts t = 0 fifteen minutes earlier. Nothing in Grünbaum's premises forbids it, since Grünbaum "only said that there was such an instant. He did not say when it was." Having shifted it once, he shifts it again, and again — days, centuries, billions of years — because at every stage it remains, by definition, an instant with no preceding neighbour and therefore no barrier. The first moment of time thus "keeps slipping away through our fingers like the bottomless pit that it is", receding into an infinitely remote past and so ceasing to be a first moment at all. The concept is self-contradictory.
2. Why space cannot grow
Antonopoulos quotes Harrison, via Tom Van Flandern, on the orthodox distinction: the Big Bang is "an explosion of space and time, not an explosion in space and time", and "the universe does not expand in space. It consists of expanding space." He replies in the literal register throughout, and deliberately so. If there is no space for the explosion to occur in, the explosion occurred in no space, hence at no place, hence — "as far as spaces, places and occurrences go" — not at all; and it would have to be "a rather small Bang. Not a big one." If it was an explosion not in time but of time, it occurred in no time, hence at no moment, hence again not at all, and it would have to be "a rather brief Bang".
The core objection concerns the verb. "Expand" and "grow" mean to take up more of space than before. A balloon can do this because it takes up more of something other than itself, and because there is always further space available to expand into. Space cannot, because Space growing means Space taking up more of Space — and at any given moment Space is only as large as it has grown and no larger, so the room required does not exist "unless of course we allow that Space is already larger than it is". By the Big Bang's own standard of what growing is, Space cannot grow.
3. The three fallacies
Antonopoulos then supplies the diagnosis. Space and Time are concepts for hetero-reference: material things, being other than Space and Time, can have boundaries in space and beginnings in time. Turn the predicates back on Space and Time themselves and the result is the same wreckage produced by turning "this proposition is false" on itself. "One's slippers are in Space, but Space itself is not in Space."
Hutten's set/member fallacy he develops with relish: the set of all false propositions is not a false set, the set of all imaginary things is not imaginary, and the set of all small things is not small — it is the largest set in existence. And self-reference, reification and the set/member confusion converge: to ascribe extension to Space is to ask "what is the extension of extension?", exactly as one might ask for the weight of Weight or the length of Length. He applies the same analysis to spatial curvature. To have a shape is to occupy some parts of space and not others; therefore if Space is curved, Space occupies some parts of Space but not others — and invoking general relativity is not a refutation, since "arguments will not be invalidated just because they happen to conflict with what Einstein — or the Pope, who is by definition infallible — have said."
He then pre-empts the obvious rejoinder, that relativistic terms are incommensurable with their Newtonian counterparts and so immune to his semantic analysis. He rejects this in two moves. First, since the Sokal affair, incommensurability has ceased to be "an alibi for meaninglessness, turned into good sense by merely switching Paradigms": any nonsense can be redeemed by redefinition — "I made a unique discovery, the discovery of a forest without trees." Second, the appeal is circular, since a theory must already be shown well-warranted before it earns the licence to change established meanings, and if the meanings are kept the theory is simply incoherent — which is the last reason to warrant it.
4. There is no such thing as "the Universe"
Drawing on Kant's Antinomies ("an absolute whole is not itself a perception"; "the totality of a series of objects is not itself an object") and again on Hutten, Antonopoulos argues that the totality shares none of the properties of its members. It has no cause: if "universe" means all the causes there are, then we have run out of causes, and asking for the cause of all causes is asking for an explanation of explaining. "If all men have a mother, then Humanity must have a mother!"
It has no age either, and here he presses hardest. "Universe" means everything that exists; so "how old is the universe?" becomes "what is the age of everything that exists?" — of near-infinitely many things each with a different age. Is that one age or many? An average would not serve, and in any case would come out at roughly half the quoted figure. What cosmologists actually do, he says, is identify the age of everything with the age of a single event, the Bang itself, "just so much as if the ages of all other things do not even concern them". They have silently converted "everything that exists" into "only one thing exists". His test case: call the thirty people in a room "the universe", meaning they are all that exists — are they now thirty-one? They are still thirty, and they still have thirty ages. Scaling to the real number of entities changes nothing. "The universe" denotes not an object but an inventory — a sweeping mental survey of all things at once — and inventories have no size. If an inventory has an age at all, it is the age of the making of it, "dating no earlier than when man first began to abstract."
5. The physics of ghosts
The conclusion turns on the popular formulation, quoted from Odenwald and Fienberg in Sky and Telescope, that the cosmological redshift "is not a Doppler shift", that light waves "literally stretch", that galaxies "are located at fixed positions in space", and that the real motion "does not involve travel through space", so that "it is not surprising that our intuition reels". Antonopoulos sets against it Lewis Epstein's 1987 letter in the American Journal of Physics, reporting that he had asked both Harrison and Kaufmann how to design an experiment distinguishing galaxies moving apart from space expanding between them, and that "neither person could answer and I suspect the question had not previously entered their minds." Antonopoulos notes bitterly that Harrison's "deplorable" passage is dated 1993, six years after Epstein's public request.
His verdict is that expansion theory needs both halves and cannot have them: the galaxies must do something, or there is no evidence that space grows; and they must stay put, or the claim collapses into the triviality that things move apart. What actually grows, in every ordinary case, "was the distance between the objects", and no one previously concluded from that that Space grows. He ends by quoting The Emperor's New Clothes in full.
Assessment
The paper's real contribution is its first argument, and it deserves to be separated from the polemic around it. The point that t = 0 lacks a lower bound, and that nothing in the stipulation "this is the first moment" fixes when it is, identifies something that popular expositions genuinely fudge. It is also a fair criticism of Grünbaum's passage as quoted, which does assert the non-existence of earlier instants without engaging the Kantian claim that temporal representation cannot be removed. Similarly, the demand attributed to Epstein — produce an operational distinction between receding galaxies and growing space — is a legitimate question about whether a distinction is physical or merely a coordinate choice, and it is one that working relativists have since answered explicitly in the affirmative direction Antonopoulos would not like: the expansion/motion split is indeed coordinate-dependent, which undercuts the popular "galaxies are stationary" formulation he attacks while leaving the underlying model untouched. And his hostility to incommensurability as an all-purpose alibi is well taken; a theory should not be able to immunise itself by declaring its terms untranslatable.
The central weakness is that the arguments are addressed almost entirely to prose about cosmology rather than to cosmology. The Friedmann–Lemaître–Robertson–Walker model does not say that space "takes up more of space"; it says that the metric contains a time-dependent scale factor a(t), so that the proper distance between comoving worldlines increases with cosmic time. That is a statement about a distance function on a manifold, and no part of it requires an ambient space to expand into or an inventory to enlarge. Antonopoulos's balloon objection is decisive against the balloon analogy and inert against the mathematics the analogy was meant to illustrate — a point he cannot address because he refuses, as a matter of method, to look at the mathematics at all. The same applies to curvature: intrinsic curvature was defined by Gauss and Riemann precisely so as not to require an embedding, so "Space occupies some parts of Space but not others" does not follow, and the objection would equally forbid saying that a two-dimensional surface has intrinsic curvature. His refusal to allow relativistic terms any redefinition converts what could have been a fair complaint about popularisation into a rule that no theory may introduce a technical sense of an ordinary word — which would bar most of physics since Newton.
The t = 0 argument, though the best in the paper, also has a specific hole. It assumes that a moment must be fixed by neighbours on both sides, then infers that a moment with only one neighbour can be slid freely. But t = 0 in the model is not located by a preceding instant; it is located by its metric relation to every later instant — it is the unique point from which a given proper-time interval separates any given event. A half-open interval [0, ∞) is not indeterminate at its lower endpoint merely because nothing lies below it, any more than zero is indeterminate among the non-negative reals. Antonopoulos's slide requires that translating the whole series be undetectable, and it is not: shifting the origin fifteen minutes earlier would change the elapsed time to every subsequent event, which is measurable. The argument thus turns on treating temporal order as the only structure time has, when it also has metric structure.
The set/member arguments are stronger, and the point that "the age of the universe" is a term of art rather than an average of the ages of things is correct as far as it goes, though it is a criticism of the phrase, not of the quantity. Cosmologists do not claim that everything is 13.8 billion years old; they report the proper time elapsed along a comoving worldline since a = 0, which is a well-defined number regardless of whether "the universe" names an object. Against the actual observational structure of the subject — the Hubble relation, the thermal spectrum and anisotropies of the cosmic microwave background, the light-element abundances, and the (1+z) time dilation of Type Ia supernova light curves, which is a direct measurement of the stretching Antonopoulos calls incoherent — the paper says nothing whatever. That silence is deliberate and consistent with its method, but it means the paper cannot function as the refutation it announces itself to be.
Finally, the tone works against the case. "The physics of ghosts", "the physics of desperation", the digs at Einstein and the Pope, and the closing recitation of The Emperor's New Clothes will persuade only readers already convinced, and they obscure the two or three genuinely sharp philosophical points the essay contains. The t = 0 argument and the Epstein challenge deserved a cooler setting.