Hitoshi Kitada (hitoshi@kitada.com)
Wed, 24 Mar 1999 15:20:05 +0900
Dear Stephen,
snip
>>
>[HK]
>> First a quotation from Unruh:
>>
>> >From W.G. Unruh, "Time, Gravity, and Quantum Mechanics" (gr-qc/9312027,
page 39)
>>
>> > III) Probabilities:
>> > One of the suggested resolutions of the problem mentioned above is to
select
>> > one of the variables of the unconstrained theory is selected as the time.
>> > The physically intuitive reasoning is that time in reality is an
>> > unobservable feature of the world anyway. What actually passes for
>> > time is the reading on various and sundry pieces of physical apparatus
>> > called clocks. If you as a child are late for school, it is not because
>> > your arrival at the school is late in relation to any abstract notion of
>> > time. It is rather that the reading on the face of your teacher's watch
is later than
>> > the reading at which school was supposed to start. Note that this
approach is in direct
>> > contradiction to Newton's approach as stated in the quote which began
this paper.
>
> This is a very important thought! :) But we need to note that clocks
>have no memory, thus do not define histories... Such are defined by
>relations between clocks, but we need a way of defining memory in a
>generic way...
>
>> > Time, according to the proponents of this view is exactly the common
view,
>> > and Newton's non-relationist view is wrong.
>> > The key problem with this approach is that it removes the foundation for
>> > the third aspect of time in quantum mechanics. At any one time, any
variable has
>> > one and only one value. It is this which physically justifies the whole
Hilbert space
>> > structure of quantum mechanics. But any real physical watches are
imperfect. It can
>> > be proven that any realist watch not only has a finite probability to
stop, it has a finite
>> > probability to run backwards. Now as long as the watch is simply the
measure of some
>> > outside phenomenon, one could take these probabilities into account. If,
however,
>> > time is {\bf defined} to be the reading on the face of the clock, the
question
>> > as to whether or not the clock can stop or run backward is moot--- it
cannot
>> > by definition.
>>
>> The local time of each local system is defined as the reading of the local
>> clock of the LS in Local Time theory. Thus in the sense of Unruh above, the
>> direction of time is unique for each local system.
>
> Ok, I understand that; but it seems that Unruh is assuming a
>"common
>basis" or frame of reference for the clocks to synchronize to. The fact
>that clocks can run at different speeds or have different probabilities
>of stopping is not relevant here... it is the 'direction" of the
>times... I am thinking of a time as a vector not as a scalar quantity!
How do you give a property of vector to time? Have you not ever said that time
has two possible directions--past and future?
>
>> Let us consider two LSs, say L1 and L2, and let them observe the same local
>> system L other than them. The observed phenomena and values of L are
>> transformed from the data observed by L1 to the data observed by L2 in
>> accordance with the general relativistic transformation of coordinates (by
>> Axiom 6 of LS theory). Thus two observations by L1 and L2 give the same
>> direction concerning the observation of LSs (like L) other than L1 and L2.
>> (Here the use was made of the argument by Hawking and Ellis, p. 181 to show
>> the orientability of manifold.) This implies that the arrow of all local
times
>> inside local systems coincide with each other.
Here it is unnecesary to refere to Hawking and Ellis. Just the covariance
between two LSs gives the coincidence of the directions of time of two LSs.
Thus the following criticism does not apply to the argumement above.
Also note that Hawking-Ellis discuss the orientability of time, not of
manifold. I missed this point in the previous post.
>
> Right, but this arguments about manifolds is assuming that all
>the
>clocks (here LSs) are "on one and the same manifold." This is the one
>aspect of the Local Times theory that I have some difficulty with. While
>I agree that there are an infinite number of LSs, simply mapping them to
>a single Riemannian manifold X is problematic. Since, as we have
>discussed before, we postulate no connection between the LSs, we are
>free do define an infinite number of different Xs depending of an
>arbitrary choice of connection. Such connections and their accompanying
>metrics define a <<physics>>, since the transformations *allowed* by the
>geometry are the <<physics>>! This follows from the relationship between
>the group theoretical properties of the <<physics>> and the
>corresponding geometry, which is "spacetime" in the usual consideration!
> This speaks to the idea of <<physics>> as constructed, not as a
>priori
>imposed apartheids. Please read Pratt's ratmech.ps!
>http://boole.stanford.edu/chuguide.html#ratmech
> Another way of thinking of my question is to consider the phase
>space
>of a n-body system of particles S. We can partition S up into subspaces
>S_i depending on the relative orientation of the flows in S. But note
>that to do so we start by superposing some arbitrary basis with which to
>define a coordinate system.
> I think that it would be consistent to posit that independent of a
>particular configuration and propagator, just as we can identify LSs to
>individual points in an arbitrary Riemannian manifold X, we can also
>identify an arbitrary X to each point in an LS! I believe that this is a
>duality that needs to be axamines carefully!
>
>> Here we used: firstly that the direction of local time inside a local
system
>> is unique _by definition_, and secondly that the manifold that satisfies
the
>> _GR axioms_ is orientable. So it might be said that our argument is also
based
>> on assumptions (i.e. GR axioms), but these assumptions seem to be natural
>> requirements.
>
> The "direction" of the time of an arbitrary LS is much like that of an
>arrow in an empty space, devoid of any features, it is not *observable*
>in itself; we always require a basis to orient the arrows. The
>orientability of GR manifolds, I think, is refering to a topological
>property such as we find when comparing Moebius loops to simple loops:
>
>A-------B
> | |
> | | Identifications: Moebius: A <-> D, C <-> B, Normal: A <-> B,
>C <-> D
> | |
>C-------D
>
>But note (!) without "parallel transport" and a way of "connecting the
>points", e.g. a connection, this property is unknowable! A set of
>disconnected points has very limited properties!
> The axioms of GR are only one of many possible assumptions. We must not
>assume that our experinces are the only one's possible! I understand
>that you wish to only deal with explaining that we can observe here and
>now, but a good model of physics will enable us to extend our
>understanding and thus our ability to observe/predict even more, and
>that, I believe, is the main reason to do this work. :)
>
>[SPK]
>> >There is more to this! The 'selection' of actual observations from the
>> >ensemble of possibles demands are more careful consideration. Bohm
>> >mentions a "contact matrix" C_ij in The Undivided Universe pg.377 that
>> >might give us some clues. :) I have mentioned this before and had no
>> >response. This relates directly to my posts about Weyl's gauge invariant
>> >theory.
>> > While the emission and absorption of photons (and any other particle
>> >for that mater) is well modeled by QM within LSs, the "propagation" and
>> >"dispersion" 'between' LS is not. This related to the Robertson-Walker
>> >metric question... How relativistic "corrections" are made upon
>> >observations of EMF is in need of careful study.
>> > There is also a need understand the difference between the mass terms
>> >in the internal LS Hamiltonian, such as that you gave above, and the
>> >mass terms used in the "center of Mass" relativistic corrections. We
>> >have a difference between internal "mass" and external "mass." The V(x)
>> >term seems to 'tie' together the particles; could we describe/model this
>> >internal/external relation with some fucntion of it?
>> > Since QM particles inside the LS can have infinite velocity, how do we
>> >account, if at all, for inertia, e.g. resistence to a change in state of
>> >motion. One of the goals of QG is to account for mass and inertia,
>> >which, up to now, are "penciled in." Also, do we have a way of
>> >predicting the Unruh effect within LS theory?
>> >
>> >Onward!
>> >
>> >Stephen
>> >
>>
>> I would comment on other points when I can understand the questions or
>> problems you raised.
>>
>> Best wishes,
>> Hitoshi
>
> Could we discuss the internal and external definitions of mass? Some
>people have been proposing that mass is defined in terms of zero point
>energy. Do we have a way of thinking of such in our model?
>
>http://www.stardrive.org/hrppaper.shtml
>
>Onward!
>
>Stephen
>
Best,
Hitoshi
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