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From: Michael Deckers <Michael.Deckers_at_fujitsu-siemens.com>

Date: Wed, 11 Jan 2006 17:42:54 +0000

On 2006-01-11, David Malone wrote:

*> [A lot of discussion on this list seem to revolve around people
*

*> understanding terms in different ways. In an impractical example
*

*> of that spirit...]
*

Anyway: excuse me for repeating some basics of classical mechanics;

but I believe it to be necessary.

*> To say if TAI is a monotone function of UTC, you need to put an
*

*> order on the set of possible TAI and UTC values. To say if UTC is
*

*> a continuous function of TAI, you need to put a topology on both.
*

Yes: there is an order on the set of values of timescales -

it is a basic property of spacetime models that one can distinguish

past and present, at least locally. Spacetime is a differentiable

4-dimensional manifold, its coordinate functions are usually two

times differentiable or more. In particular, the set of values of

timescales does indeed have a topology (which is Hausdorff).

*> To me, TAI seems to be a union of copies of [0,1) labelled by
*

*> YEAR-MM-DD HH:MM:SS where you glue the ends together in the obvious
*

*> way and SS runs from 00-59. You then put the obvious order on it
*

*> that makes it look like the real numbers.
*

TAI is determined as a weighted mean of the (scaled) proper times

measured by an ensemble of clocks close to the geoid - so the

values of TAI must belong to the same space as these proper times,

which (being line integrals of a 1-form) take their values in the

same space as the time coordinates of spacetime (such as TCB and TCG).

No gluing is needed. And yes: this space is diffeomorphic to the

real line.

All of this is completely independent from the choice of a particular

calendar or of the time units to be used for expressing timescale values.

*> OTOH, UTC seems to be a union of copies of [0,1) labelled by
*

*> YEAR-MM-DD HH:MM:SS where SS runs from 00-60. You glue both the end
*

*> of second 59 and 60 to the start of the next minute, in adition to
*

*> the obvious glueing.
*

*> I haven't checked all the details, but seems to me that you can put
*

*> a reasonable topology and order on the set of UTC values that
*

*> will make UTC a continious monotone function of TAI. The topology
*

*> is unlikely to be Hausdorf, but you can't have everything.
*

If you subtract a time from a timescale value, you get another

timescale value. If you mean to say that UTC takes its values in a

different space than TAI then you cannot agree with UTC = TAI - DTAI,

as in the official definition of UTC. And if you say that

UTC - TAI can be discontinuous (as a function of whatever)

with both UTC and TAI continuous then you must have a subtraction that

is not continuous. Strange indeed. Where did I misinterpret your post?

And can you give some reference for your assertions?

Michael

Received on Wed Jan 11 2006 - 09:43:22 PST

Date: Wed, 11 Jan 2006 17:42:54 +0000

On 2006-01-11, David Malone wrote:

Anyway: excuse me for repeating some basics of classical mechanics;

but I believe it to be necessary.

Yes: there is an order on the set of values of timescales -

it is a basic property of spacetime models that one can distinguish

past and present, at least locally. Spacetime is a differentiable

4-dimensional manifold, its coordinate functions are usually two

times differentiable or more. In particular, the set of values of

timescales does indeed have a topology (which is Hausdorff).

TAI is determined as a weighted mean of the (scaled) proper times

measured by an ensemble of clocks close to the geoid - so the

values of TAI must belong to the same space as these proper times,

which (being line integrals of a 1-form) take their values in the

same space as the time coordinates of spacetime (such as TCB and TCG).

No gluing is needed. And yes: this space is diffeomorphic to the

real line.

All of this is completely independent from the choice of a particular

calendar or of the time units to be used for expressing timescale values.

If you subtract a time from a timescale value, you get another

timescale value. If you mean to say that UTC takes its values in a

different space than TAI then you cannot agree with UTC = TAI - DTAI,

as in the official definition of UTC. And if you say that

UTC - TAI can be discontinuous (as a function of whatever)

with both UTC and TAI continuous then you must have a subtraction that

is not continuous. Strange indeed. Where did I misinterpret your post?

And can you give some reference for your assertions?

Michael

Received on Wed Jan 11 2006 - 09:43:22 PST

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