With General Relativity, time is so geometrical that you can make it
(Cf the Gödel's solutions to Einstein's GR Equation, which gives hope
to some to build a time machine, and even infinite computers!).
Give me just a sufficiently massive cylinder ...
On 06 Jan 2009, at 12:51, Bruno Marchal wrote:
> I agree with Brent. In relativity theory space and time are
> intermingled in a geometrical way to give the Minkowski structure.
> Actually you can make it into an Euclidian space by introducing an
> imaginary time t' = sqr(-1)*t = it. The metrics becomes dx^2 + dy^2 +
> dz^2 + dt'^2.
> In quantum mechanics the possible position of an object on a line
> rise to an hermitian space: it is infinite dimensional, but there is
> still a geometrical structure, with notions akin to angles and
> distances. Of course mathematician have far more general notion of
> dimensional spaces, some of which have nothing to do with geometry. In
> physics metrics play always some role somewhere though.
> Le 06-janv.-09, à 02:59, Brent Meeker a écrit :
>> Abram Demski wrote:
>>> If time is merely an additional space dimension, why do we
>>> "moving" in it always and only in one direction? Why do we remember
>>> the past and not the future? Could a being move in some spatial
>>> dimension in the same way we move through time, and in doing so
>>> time more like we treat space? Et cetera.
>>> To my knowledge, modern physics treats many things as "dimensions":
>>> not just time and space, but also forces such as electromagnetism.
>>> This does not imply that such things are spatial in nature. A
>>> dimension is just a variable. Unless you think there is something
>>> particularly spatial about time?
>> There is something spatial about time, duration is measured along
>> paths in
>> space. Coordinate time is mixed with space by Lorentz symmetries.
>> But it's
>> still different from space. Lee Smolin and Fotini Markopolo have
>> argued that
>> time must be considered fundamental (no block universe).
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