1

In physical terms, continuity refers to smooth change of something through time.

To go from nothing to something surely is a non-smooth event, a discontinuous change.

So if continuity is to be followed, we must have 'from nothing comes nothing'.

Also, can we say that continuity is a more basic principle, or at least on a par with nothing - as it can be used to establish its invariance in time.

Of course this is not a mathematical argument - and can't be understood rigourously.

More fundamentally, if one has nothing, then one also has no time either. So its a triviality that 'from nothing, nothing'. So in the argument should one allow at least both space and time?

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One must be careful of what qualities one thinks of as being subject to a continuity constraint, or else one obtains Zeno-like paradoxes.

Is the transition from "nothing" to "something" necessarily discontinuous? Physically realistic or no, I can certainly imagine a vacuum slowly producing a continuous substance (i.e. not composed of atoms) starting at some time T, so that as one considers times arbitrarily soon after T one finds arbitrarily little of the substance. Thus the amount of the continuous matter itself varies continuously with time.

There are two criticisms that I can think of concerning this. One is that it violates modern ideas about physics (which is of course atomistic), and the second is that even in this case there is a transition from "nothingness" to "something" at time T which is not affected by the fact that there is initially very little of that "something". I address these as follows.

  1. At issue here is how specific one wants to make the metaphysical argument. Do you want a priori principles, or not? Suppose however that you are indeed attempting to justify this old principle on new grounds. The question then arises as to what sort of continuous changes you admit. After all, quantum mechanics is a continuous theory dealing with discrete changes: how is it that it admits the possibility of change with time? The answer is: by continuous change in amplitudes, the quantities which give rise to the probabilities of various outcomes in a physical process.

    How this plays out, for instance in nuclear decay (a process in which we may smoothly transition from having none of some nuclear decay product, to some of it) is that there is a continuously evolving probability of some process occurring in the nucleus, which causes some particle(s) to be ejected. If you imagined continuously observing some atom in a non-disturbing way, the transition would appear to be discontinuous; but it nevertheless came about by a continuous process to the best of our knowledge.

    You might complain that this is still at its root discontinuous, as evidenced by my description of continuous observation. Setting aside the fact that this seems anyway to be how quantum mechanics works (by continuous evolution of amplitudes between configurations which seem discrete) and that it's up to oneself how to come to grips with it, there's also a problem with the "continuous observation" description that I gave. That is, no observation is non-disturbing; and in this case the effect of continuous observation would be to prevent any change. This is known as the quantum Zeno effect, and leads me to the second criticism.

  2. At issue here is that there are changes which seem discontinuous to us at first glance, but may be an artificial distinction of our own making. A similar, but more poignant example than nuclear decay is simple motion through space.

    Achilles stands to my left. He shoots an arrow at a target, to my right. (I stand outside of the line of fire for the purposes of this argument.) If Achilles aims truly, the arrow — specifically the tip of the arrowhead — eventually changes from being on my left to being on my right. Is this not a discontinuous change? Even if you grant that for some time between it is in front of me, that just replaces one discontinuity (left/right) with two (left/front, front/right). Indeed, if space is made of distinct points, then there is a continuum of discontinuities, as the arrowhead passes between points. Then how is motion possible?

    The modern answer is that the points in space are distinct, but not equally so: points which are closer together are "less different" than points which are further apart. This is after all the root of the concept of the continuum. Similarly, the distinctions left/front/right are artificial: not meaningless, but nevertheless ones introduced by ourselves, and coarser than the reality we attempt to describe. Not all points "in front" of me are equivalent, so I should not be shocked when the arrow comes to be in front of me when previously it was on my left.

    Even in quantum mechanics there is a puzzle to be solved with respect to the nature of time: it is not possible so far as we know to define "the point in time that the arrow passes in front of me" as a crisply defined physical observable, because continuous observation of a sharply defined region of space in front of me would actually prevent the arrow from entering that space! (Here I obviously don't refer to casual observation with the eyes, but a hypothetical apparatus which instantly detects any intrusion by the arrow into the space — which, in doing so, ironically creates an impregnable barrier to entry for the arrow.) One simple solution is that such rigorous and acute observation is impossible; which may well be described as a consequence of the (infinite) energy demands necessary to make observations of unlimited precision, to distinguish sharply between two "régimes" which meet at a thin boundary.

    Similarly, the transition from "nothing" to "something" is a binary distinction which we are making about possible worlds, in which not all amounts of "something" are equally distinguishable from "nothing". As my example of Achilles shows, if you impose such binary distinctions too dogmatically, you may have to accept an apparently discontinuous description of the world as the price of your insistence, in order to avoid paradox.

In short, unless you stipulate very precisely what you imagine the world to be like (that is, present the question as one of physics rather than metaphysics), a principle of continuity such as you describe is not enough to prevent the emergence of something from nothing, unless it also prevents change even in worlds with something.

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