From: jos.bergervoet@xs4all.nl
On 7/31/2017 1:35 PM, Thomas Koenig wrote:
> J. J. Lodder schrieb:
>
>> For example, is a centimeter compatible with a nanosecond?
>> No, of course not, well indoctrinated kiddies will tell you
>> with the wisdom of 1793.
>> However, these days the nanosecond equals 29.9792458 cm (exactly)
>
> Time certainly doesn't equal length,
Then height doesn't equal width. And you might just
as well use the 'fathom' to measure the former and
the 'furlong' for the latter.
> and trying to use definitions
> of units in such a way is misleading at best.
On the contrary, it makes clear that they are just
4 coordinates on a 4-dimensional manifold.
> Otherwise, tell me what reasonable result you get if you add a
> second to a meter.
More reasonable is to compute time^2-length^2 (the
metric in our universe). Having the same units in
that case saves you applying a conversion constant.
>> In a very real sense the metric system came too early.
>> (before the relevant physics was well enough understood)
>> If we could start all over again
>> there wouldn't be a separate length unit at all.
>
> It is certainly useful to have both; if only to avoid the mistake
> of adding a length to a time.
Sometimes it makes sense to use separate units for
the coordinates, but not if the manifold is very
much curved (e.g. if you move to a Schwarzschild
radius time and space will reverse roles..)
For ploughing furs with a span of oxen, on the other
hand, the furlong is of course useful (and was
invented for it!) but only if you do not use it for
the height coordinate (the oxen would agree with you
that there is a difference). It all depends..
--
Jos
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