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The special relativity theory teaches us that simultaneity is relative to the motion of our reference frame. This seems to contradict the intuitive notion of the present to be instantaneous. Some additional paradoxes from quantum mechanics and general relativity seem to question our intuitive notion of time and present even more so that a static deterministic universe seems to be the only consistent solution compatible with these experimentally well confirmed paradoxes.

However, assume that we are convinced that the universe is dynamic and non-deterministic. Are there any specific properties of the present, like being instantaneous, that are necessarily implied by this? Even if we say that the present is the interface between the past and the future, does it really follow that this interface must be infinitely sharp?

At least for computer simulations of hyperbolic partial differential equations, it can sometimes be convenient to use a multistep scheme, or to use a position dependent time shift (for simulating oblique incidence on a periodic structure). However, this computer simulation is effectively analogous to the static deterministic universe, hence it is unclear what we can really conclude from this for the dynamic non-deterministic case.

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    Is this really a philosophy question, or a physics question? – Michael Dorfman Aug 20 '12 at 8:29
  • @MichaelDorfman I doubt that this is a physics question. This doesn't mean that it is necessarily a philosophy question. Also consider that "we don't know" or "we don't care" can be a valid answer to such a question. Perhaps a physicists has less problems giving such an answer, because he sees no need to justify this answer. Perhaps a similar philosophical answer would be to point out that the meaning of "dynamic and non-deterministic" is undefined in this context. – Thomas Klimpel Aug 20 '12 at 9:15
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    @MichaelDorfman: this question is not really bounded by any particular physical framework I know of. I'd class it as philosophy inasmuch as it is metaphysics. However, it does require an answer which can distinguish what is essential about a nondeterministic dynamic universe which would distinguish it from a deterministic one with respect to the notion of time, aside from the obvious one that there is not a single necessary evolution in time. This question has potential, but is perhaps a bit ambitious! – Niel de Beaudrap Aug 20 '12 at 10:06
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    One specific criticism that I would level -- how would you go about defining past and future? If I were to consider how I would describe these, it would be in terms of the present, not vice versa. This makes the notion of "the present" perhaps trivial, like that of "the natural" to a philosophical materialist. In that case, you should clarify what you mean by non-instantaneous, i.e. what does it mean for the present to not be instantaneous, if the past and future are defined with respect to the present, and not usable as primitve concepts in the notion of 'not instantaneous'? – Niel de Beaudrap Aug 20 '12 at 10:16
  • @NieldeBeaudrap I think the past is what has happened already, and the future is what has not happened yet. A river is often used as an analogy for time. The past is the water downstream (which won't pass by again) and the future is the water upstream (which has not passed by yet). The definition of the present in this picture is less obvious to me. – Thomas Klimpel Aug 26 '12 at 20:07
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That we perceive the present as instantaneous is dependent not on special relativity or on events comparable in duration to the time it takes light to cross the width of our heads (nanoseconds), but on the relatively slow conduction of action potentials in our neurons (milliseconds).

Given that everyone manages to maintain a percept of instantaneity in the face of the inability of their brain's to communicate with itself for such a long time, we can't rely upon intuition for much help here. What appears to us to be the instantaneous present is a collection of different events causally disconnected for milliseconds at least.

Having dispensed with intuition, we then are left with a pure physics question: is a dynamic non-deterministic universe required to have an instantaneous present if it is to agree with experimental observations? And there the answer is a resounding sort of. Bell's inequality already argues that the universe is best modeled as non-deterministic (at the quantum mechanical level). Whether something is "dynamic" or "static" seems unlikely to have a bearing unless you make up rules that force it to be one thing or the other. (E.g. if by "dynamic" you mean that the rules change as a function of time, and you insist that time is a global variable instead of a point variable coupled to adjacent points in some way, then you have by your definition imposed a necessarily instantaneous present coupled to your postulated variable.)

Experimental observations are consistent with a loose idea of "present", since state transitions occur in finite space and therefore in finite time, and since they have finite energy they are delocalized in time according to the uncertainty principle.

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Q: The special relativity theory teaches us that simultaneity is relative to the motion of our reference frame. This seems to contradict the intuitive notion of the present to be instantaneous.

As far as I am aware, simultaneity in special relativity is about distance-separated events appearing to be simultaneous or not simultaneous depending on the observer's frame, and the frame is only affected by the speed of light limit.

Therefore, events actually happening simultaneously in the present may later appear to be simultaneous or not simultaneous to moving observers. This does not materially affect the notion of the present as instantaneous so there is no contradiction.

https://en.wikipedia.org/wiki/Relativity_of_simultaneity#Explanation

Different observers' frames are different due to the speed of light limit.

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Worldline of particle or observer's frame moving with speed v less than c.

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