Problem of Time II
As indicated by the outside of an astrolabe disc, whether in hours or months, time divisions are defined in terms of periodic motions in the heavens. Time lies on a discrete circle before a continuous one, since measurement never resolves the intervals indefinitely. Yet even before astrolabes, and modern science, Zeno proposed the riddle of Achilles and the tortoise, relying not on a continuous time, but on the assumption of an infinitely divisible space.
Why should space appear infinitely divisible when time does not? Of course, for the purposes of 19th century physics, the continuum is a useful construction, but now one expects this classical geometry to emerge (ie. be derived) from a collective of the large scale observations of like observers, such as ourselves. If so, where does the notion of scale originate? To begin with, we are now used to the correspondence between cosmic time and cosmic scale in an expanding cosmology, so we can ask instead: from where does our notion of cosmic time originate? We immediately observe that an estimate of cosmic time is something that, as sensible observers, we are largely in agreement upon.
What does it mean to view this kind of time on a discrete circle? We are not talking about cyclic universes, or any construction that proposes structure outside what we can possibly observe. So discrete cosmic time is a concept of quantization on cosmic scales. This sounds a bit like the old style Bohr correspondence, which after all had a good phenomenological basis. Now let us not assume that this cosmic time is universal for all observers. Then its range of values is analogous to the quantized energy levels of a hydrogen atom.
Why should space appear infinitely divisible when time does not? Of course, for the purposes of 19th century physics, the continuum is a useful construction, but now one expects this classical geometry to emerge (ie. be derived) from a collective of the large scale observations of like observers, such as ourselves. If so, where does the notion of scale originate? To begin with, we are now used to the correspondence between cosmic time and cosmic scale in an expanding cosmology, so we can ask instead: from where does our notion of cosmic time originate? We immediately observe that an estimate of cosmic time is something that, as sensible observers, we are largely in agreement upon.
What does it mean to view this kind of time on a discrete circle? We are not talking about cyclic universes, or any construction that proposes structure outside what we can possibly observe. So discrete cosmic time is a concept of quantization on cosmic scales. This sounds a bit like the old style Bohr correspondence, which after all had a good phenomenological basis. Now let us not assume that this cosmic time is universal for all observers. Then its range of values is analogous to the quantized energy levels of a hydrogen atom.
posted by Kea | 8:22 AM
3 Comments:
A particularly thoght-provoking post today! Perhaps we will one day discover some quantum nature of time.
Now let us not assume that this cosmic time is universal for all observers. Then its range of values is analogous to the quantized energy levels of a hydrogen atom.
Kea: Discretization of time makes sense but are you saying that the mathematical formalism for such quantization is similar to the quantization of energy levels for H atom? Or are you simply comparing these concepts abstractly? Curious thanks.
Hi Mahndisa. I guess I'm saying that a suitable abstraction of the mathematical formalism of the hydrogen atom, naturally involving lots of category theory, is a good way to look at a discretised time. But note that our view of cosmic time is strictly outside of ordinary low E quantum mechanics, and requires some input from quantum gravity.
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