**Stephen P. King** (*stephenk1@home.com*)

*Thu, 25 Mar 1999 13:58:22 -0500*

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Dear Hitoshi and Robert,

I am combining your posts to respond to them.

Hitoshi Kitada wrote:

*>
*

*> Dear Stephen,
*

*>
*

*> I need to ask your definition of "the arrow of time."
*

My definition of "the arrow of time" is the fact that events are

experience in a sequence, a flow of causality and inference, not just a

one-dimensional chaining like points in R^1, but more like a concurrency

of becoming, actions leading to actions. I feel that the typical

modeling of time fixes itself on just one "path" like the shortest path

between vertices in a graph and is myopic to all other paths. Another

aspect of "the arrow of time" is the correlation between its "direction"

and the choice of a maximum entropy state for the systems being

observed. Many have said that entropy *is* the arrow of time, and in a

sense I agree; this leads to my thinking of computational complexity and

Maxwell's daemon in order to make sense of this and try to build a

coherent and pragmatic understanding of time.

*> Reading your comments again, I feel that your stand is slightly different from
*

*> mine. I feel this in that
*

*>
*

*> > That is the same as saying that an arrow has two directions of possible
*

*> >motion: forwards and backwards. We fail to see a vector like quantity of
*

*> >time when we forget that one CAN NOT assume an a priori ordering to
*

*> >events "in time!" The totality of Existence has *no* inherent orderings!
*

*>
*

*> and somewhere else in the following quotation. I do not speak of "the
*

*> direction of time" valid throughout the total universe. Just the direction is
*

*> useful for each group of observers, whose times are defined as real parameters
*

*> of motion inside each local system. But seeing that you state that time is a
*

*> vector or something like that, I feel your definition of time would be
*

*> different from mine.
*

Forgive me for not being clear. :( This 'vector'-like aspect is

an

attempt to think about how LS interactions bring about a coherent

definition of time within the context of the interactions/communications

between LS. This aspect is classical. What you state above: "real

parameters of motion inside each local system" is the internal QM aspect

and I agree with it completely! I am trying to understand the external

aspect. We seem to agree that the typical GR model (field equations,

etc.) are lacking, and thus I am trying, at least from a philosophy of

science stance, to model a broader range of phenomena.

*> I agree with "The totality of Existence has *no* inherent orderings!" and with
*

*> "our "view of the cosmos" is *not* "the cosmos"!" My notion of time is the
*

*> clocking of each local system. Direction is asked only when one system sees
*

*> its outside to find other systems' events occur in accordance with the order
*

*> of its observer's system. In other words this stand is the one that admits
*

*> what is important is subjectivity. My argument about the direction of time in
*

*> these posts is one of the supports for this importance of subjectivity. I.e.
*

*> my claim is that the direction of time obeys us.
*

I have understand the importance of subjectivity for a long

time! :) It

is impossible to be strictly "objective", this is what Newton tried to

do

and failed, but strict subjectivity is equally impossible. The concept

of "solipsism" speaks to this.

I believe that there are key aspect to: "Direction is asked only

when

one system sees its outside to find other systems' events occur in

accordance with the order of its observer's system" that need to be

better understood. There is details here that need to be explored, since

the questions of how communication and consciousness are possible. Let

me elaborate:

Starting with your words: "Direction is asked only when one

system sees

its outside to find other systems' events occur in accordance with the

order of its observer's system"

I would argue that the information about observations of any

given LS

of "its outside" are a function of the possible information that is can

encode in its configurations. This is analogous to how a computer can

only compute with a programming language that is consistent with its set

of possible states or like a person can only speak about situations that

it can describe using sounds and symbols within its repertoire of

experience.

When LS "observe" each other, they do not <<see>> all possible

configurations of the center of mass (I would add charge and angular

momentum to this!) of other LSs, their observations are restricted to

those that are consistent this their internal information, which given

their faintness, is finite and thus we get under assumptions of binary

logic, disjointness of their information. I argue that still is

restrictive and needs to be weakened to allow for the possibility of

mutual subsethood. We can retain separate identity of local systems if

we can show that LS differing in at least one subset, a singleton, are

disjoint, but not is a binary mutual exclusion kind of way.

This consideration has formalisms already "out there" that we

can "plug

in", others, such as Bart Kosko has already established the mechanism.

We only need to be able to translate our jargon and realize that there

is not *unique* set of *mathematical* symbols that represent a

consistent unification of QM and GR. An example of this is illustrated

by the many axioms in logic and geometry that are not consistent with

each other but allow for the construction of self consistent formalisms,

such as the axiom of choice, the parallel postulate, etc. The Universe

contains them all!

*> I agree that there is other possibility which allow the existence of many
*

*> sheets of the world. Manifold X may be replaced by "superspace," as you say.
*

*> My assumption may be in that there is a common framework for a finite number
*

*> of observers that allows to compare the directions of time among these LSs.
*

*> But I do not say more than this. Maybe the manifold X in the introduction in
*

*> my papers might have misled you to think that I assume one single universe.
*

*> But what I proposed as a problem is the finiteness of the ability of human
*

*> beings, thus I do not consider the direction of time on X. Just I said that if
*

*> it could be possible as Einstein's theory to speak about one single universe,
*

*> then the direction of time would be common for all observers (of infinite
*

*> number). In this respect I admit that I might have been influenced by the
*

*> Einstein's theory.
*

:) I understand your stance in using a single manifold X, it

well

illustrates the problem of time and a very good and consistent solution,

but we must extend it further if we are to compete successfully with the

likes of Puthoff and Hawking. I can understand that "this is your baby"

and may not like people like me altering it and using it, but let me

assume you that I have the utmost respect for you and your hard work! I

am very honored by your consideration of my silly ideas. :)

I am trying to extend your theory further. This should be

expected

since we have discovered a similar idea independently! :) My work is not

mathematical, it is philosophical, thus I bow to your excellent

abilities in the mathematics of scattering and other areas. I also have

friends that are researching Clifford and Grassmann algebras and

geometries, which seem to give us a way of modeling LS interactions in a

way that extends GR, much like it extended the Newtonian model. We also

have Robert understanding of computer programming and knowledge of

digital signal processing (DSP) with also helps. I see us as a team each

with our own abilities and specializations and by working together we

can accomplish that we can not individually.

*> I have not had hope for sciences, as I may have written before to you and
*

*> Robert. The "meta sciences" means "after sciences." If human beings could find
*

*> something new about time, it would be a technological evolution. Even a time
*

*> machine would be a technology if it would be possible. Remember that atomic
*

*> bomb was a result of technology. The mere Einstein's letter to the President
*

*> could not realize that. That letter was working just as a leading slogan. I do
*

*> not admit the usage of the bomb at the age. But technology could be a remedy
*

*> for our future at any age as well as for the present difficult age. Sciences
*

*> would be just a spiritual support for such technologies. My hope for meta
*

*> sciences is the learning of human beings about themselves, not for any new
*

*> sciences and technologies. Human beings need to learn to be safe in mind even
*

*> if they know that they are local existence, who are not able to become a god.
*

*> Sciences seemed to have made people think human beings are belonging to the
*

*> race of God. My recognition is that any mighty power that sciences give human
*

*> could not give them the position of God. God can be attained only by knowing
*

*> the finiteness of themselves. To know we are finite beings is the meta
*

*> sciences.
*

*>
*

*> Best wishes,
*

*> Hitoshi
*

What we are working toward, IMHO, is the ability to control

gravity and

its dual, inertia. This is "Star Trek" technology!

*> -----Original Message-----
*

*> From: Stephen P. King <stephenk1@home.com>
*

*> To: Hitoshi Kitada <hitoshi@kitada.com>
*

*> Date: Wednesday, March 24, 1999 11:00 PM
*

*> Subject: Re: [time 52] Orientation of time
*

*>
*

*> >Dear Hitoshi,
*

*> >
*

*> > Please don't lose patience with me. :) You are not understanding me...
*

*> >:( I am posting this to you alone.
*

*> >
*

*> >Hitoshi Kitada wrote:
*

*> >snip
*

*> >[HK]
*

*> >> >> 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.
*

*> >
*

*> >[SPK]
*

*> >> > 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!
*

*> >[HK]
*

*> >> How do you give a property of vector to time? Have you not ever said that time
*

*> >> has two possible directions--past and future?
*

*> >[SPK]
*

*> > That is the same as saying that an arrow has two directions of possible
*

*> >motion: forwards and backwards. We fail to see a vector like quantity of
*

*> >time when we forget that one CAN NOT assume an a priori ordering to
*

*> >events "in time!" The totality of Existence has *no* inherent orderings!
*

*> >Your argument about a problem with probabilities is an example of what I
*

*> >am talking about.
*

*> > This is one of the dangers of using a Real number (or any number system
*

*> >for that matter) for identification in H\psi = \lamba\psi in (2) of
*

*> >Axiom 1. We forget that entities do not come with labels on them: 1, 2,
*

*> >3, ,4,... for our convenience. A clock is *NOT* an ordering, it is a
*

*> >gauge of the duration between events, we do not get a unique
*

*> >transitivity property (...-> A -> B -> C->...), like Weyl's
*

*> >"order-relation" in the quote on pg. 6 of time_III.ps, with it alone!
*

*> >Such orderings are constructed in terms of inclusion given a set of
*

*> >interactions *between* LSs. This is a very subtle but important idea.
*

*> >Please read my comment carefully!
*

*> >[HK]
*

*> >> >> 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.
*

*> >[SPK]
*

*> > Here the subtle tacit assumption has entered: "let them observe the
*

*> >*same* local system L other than them". It is not correct to assume,
*

*> >that what L1 calls L is not necessarily what L2 calls L, ab initio. It
*

*> >is only via communication between L1 and L2 that they arrive on a
*

*> >consensus of what they refer to as L. This is the same as what occurs at
*

*> >the level of human conversations about entities. Your consideration only
*

*> >makes sense from the perspective of another LS L3 that can observe L,
*

*> >L1, and L2 simultaneously, and thus is imposing its own "ruler" and
*

*> >"clock" on its observation of their exteriors. I wish my friend Paul
*

*> >would release to me his papers on this, it is a fallasy hidden in GR due
*

*> >to the assumption of a unique transitive ordering of events in its math.
*

*> > It is the assumption that 'we all exist in the same universe' that is
*

*> >the cause of problem understanding time, and for that matter, space as
*

*> >well! We superpose spacetimes when we superpose wave functions and
*

*> >ignore the consequences to our detriment. It is so easy to not recognize
*

*> >that we make observations with our own unique ruler and clock and
*

*> >ordering, we forget that our "view of the cosmos" is *not* "the cosmos"!
*

BTW, this term "cosmos" that I use, speaks to what is called the

"universe" by most physicists. I have long railed against the notion

that the commonly observed cosmos of stars, galaxies and other similar

objects is *not* the only one possibly to observe! This is an example of

the assumption that what an individual observes is taken to be

*everything* and anyone's observations must be "interpreted" only with

the ruler and clock and ordering of that ideal and imaginary "one". The

idea of "manifest covarience"(1) used in relativity is an example of

this! (1 "the same laws of <<physics>> must be seem by all [possible]

observers, no matter how they are behaving") We can not just postulate

that there is <<one>> set of <<physics>> for all possible observers, but

we may show that there exist finite sets of observers that observe the

same <<physics>>. These are what make up what I call a <<cosmos>>. On an

aside, F. David Peat's discussion of Witten's M-theory and related

matters on page 312-316 of Superstrings and the Search for The Theory of

Everything shown that others are willing to question this idea of

manifest covariance as most sacred of cows!

I have been reading chapter 15 of Bohm and Hiley's The Undivided

Universe while I was with Joyce at the doctor today. Again I find myself

thinking that their "algebra of the implicate order" offers some clues

as to how to model LS interactions. I conjecture that the Hubble red

shift is an indication of how cosmoses that are increasingly different

in

their configurations and thus their information cause a "fading". Bohm

and Hiley mention something like this: (pg. 377 ibid.)

"An interesting question arises if there is no matrix C'_ij

which is

locally connected. A similar question arises in general relativity when

the metric tensor cannot be made diagonal over the whole space. In this

case we have a new property called curvature. If C_ij cannot be

transformed into a locally connected matrix, this means that we have a

'space' which may be 'locally explicate' but which gradually unfolds as

we move along [or we can parametrize motion in terms of 'unfolding'!]

the locally ordered lines. To picture this we can say that 'wherever

you are' you may represent this as an 'ordinary local space' but there

will be a horizon in which this space "dissolves" into an implicate

order. Such a 'universe' [I call it a "cosmos"] would not have a

definite boundary, but would simply fade into something that does not

manifest to us {an arbitrary observer] beyond its horizon. Nor would it

have a [definite objective and/or absolute] beginning or end. But rather

it would simply fade in the distant past and future. Yet, to anyone that

was beyond our horizon everything would be as definite (or indefinite)

as it is to us. That is to say, there is a kind of relativity of the

implicate order. Some new mathematical concept corresponding to

curvature would have to be developed to express more precisely the

distinction between an irreducibly implicate order [like our "total

Universe U!] and one that could be transformed as a whole into an

explicate order [like my concept of a cosmos].

This idea, IMHO, may be exactly what we are working on with

Local Times

theory! :) I think I have mentioned this before but it may have not have

been noticed or understood, which amount to the same thing! :)

We find that there is something like a hierarchy in the way that

LSs are

composed of independent subLSs while simultaneously there is a

composition of the classical center of masses of the LSs at each "level"

of the hierarchy. But when we consider that there is a key difference

between the internal QM perspective and the external GR (and I submit

that I am using the term GR loosely) perspective, we find that the Tree

that is constructed is not ordinary to say the least. I think that we

agree that all observations at given in terms of the external GR

perspective since the internal QM properties are, by definition,

unobservable; but we are able, as you discuss, to "infer" the QM

properties within the framework of a classical paradigm or framework.

This is an area where Matti's work is very relevant!

[HK]

*> >> 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.
*

*> >[SPK]
*

*> > The covariance between two LSs gives an agreement on the time elapsed
*

*> >(duration) of time of the two LSs. "Direction" is another matter
*

*> >entirely! My critique does apply!
*

*> >[HK]
*

*> >> Also note that Hawking-Ellis discuss the orientability of time, not of
*

*> >> manifold. I missed this point in the previous post.
*

*> >
*

*> > The orientability of time, since the manifold includes time as on of
*

*> >its components, makes my argument nontrivial. But, here we are thinking
*

*> >of time in terms of durations *and* orderings.
*

*> >[SPK]
*

*> >> > 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!
*

*> >> >[HK]
*

*> >> >> 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.
*

*> >> >[SPK]
*

*> >> > 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
*

*> >> > | |
*

*> >> > | |
*

*> >> > | |
*

*> >> >C-------D
*

*> >> >
*

*> >> >Identifications: Moebius: A <-> D, C <-> B, Normal: A <-> B, 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
*

*> >
*

*> >Onward!
*

*> >
*

*> >Stephen
*

*> >
*

And now turning to Robert's ideas! :)

ca314159 wrote:

*>
*

*> Dear Hitoshi and Stephen,
*

*>
*

*> Hitoshi Kitada wrote:
*

*> > My hope for meta sciences is the learning of human beings about themselves,
*

*> > not for any new sciences and technologies.
*

*>
*

*> I also do not see anything "mystical" going on, but I do see how people
*

*> might have developed the "god" concept from the extremes of an observation.
*

*>
*

*> What is the limit of a scientific observation ? When we perform macroscopic
*

*> observations, we allow for some subjective interpretation of the results.
*

*>
*

*> But even in quantum mechanics, subjective interpretation sneaks in. Why ?
*

*>
*

*> When a closed system is observed from the outside, are we not treating
*

*> it as a universe with ourselves in a god-like context ? In such a case
*

*> it seems, we need to understand what this means in terms of the measurement.
*

*>
*

*> When we dissect a closed system scientifically, as we understand more and
*

*> more about that system, is this the same as if we are understanding more and
*

*> more about our universe ? Ultimately reaching the limit of understanding the
*

*> whole ? Then the same subjective/interpretive problems should arise at
*

*> the microscopic level as do in the macroscopic.
*

*>
*

*> Otherwise observation, measurement and science itself is not scale invariant ?
*

*>
*

*> Should we necessarily find miniture "paintings" in the quantum domain; open to
*

*> extreme subjective interpretation ?
*

*>
*

*> This reminds me of Michel Foucault's analysis of Rene Magritte's painting:
*

*> "This is not a pipe." :
*

*> http://www.artonline.it/edicola/artdos2/059/i11m-059.html
*

*> Foucault's book is called "This is not a pipe. An art quantum"
*

*>
*

*> I don't take this lightly because it really does indicate that there
*

*> are the same interpretive problems in what might be called hard or
*

*> "pure science" as there are in the meta or "soft" sciences.
*

*>
*

*> I can't see pursuing pure science without understanding just what we
*

*> should do when we meet up with the dualisms.
*

We need to always remember that science without philosophy is mere

taxonomy!

*> Nietzsche and Ayn Rand (objectivists) warn about the mole-like
*

*> philologists who are indecisive on matters of urgency and practical
*

*> matters. Excessive context seems to breed complacency.
*

*> (That's probably why most religions prescribe six days of objective
*

*> work and one day of restful subjectivity?)
*

*>
*

*> I am still puzzling with the very first question I made on Hitoshi's
*

*> web site: that space is complementary with time. Does the presense
*

*> of fermionic matter introduce an anisotropy into this as Sweetser seems to
*

*> discribe below ? Are we considering in the time list, only the bosonic
*

*> case which does not address the (anisotropic) arrow of time ?
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I believe that just as we need a local system model of "time" there is

also a complementary local system model of "space". I think that it is

already implicit in the equations that Hitoshi discusses in his papers,

it is just that that issue has not been addressed yet. :) Hint, the way

that LS theory defines the uncertainty of time could be used to define

the uncertainty of space. This also would connect to the other canonical

conjugate variables! :)

*> > >> > Could we discuss the internal and external definitions of mass? Some
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*> > >> >people have been proposing that mass is defined in terms of zero point
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*> > >> >energy. Do we have a way of thinking of such in our model?
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*>
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*> Take a look at the "nerd" description which looks interesting.
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*>
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*> http://world.std.com/~sweetser/PopScience/speed/speed.html
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"The relativistic velocity of light is beta = 1. In differential form,

this says the amount of change in space equals the amount of change in

time. In integral form, this says the amount of space traveled by light

is the amount of time passed. What all inertial observers agree on is

the functional relation between space and time: it is one-to-one and

onto. This function is invertible and a photon is its own antiparticle.

For objects with a mass, beta < 1. In differential form, the amount of

change in space is less than the amount of change in time. In integral

form, this says the amount space traveled by a mass is less than the

amount of

time passed. There is a function that maps time onto space, but it is

not one-to-one. The function is not invertible and each particle's

antiparticle is distinct."

Could we say in this context that the change in the uncertainty of time

equals the change in the uncertainty of space, e.g. they are covariant?

Onward to the Unknown!

Stephen

**Next message:**Stephen P. King: "[time 58] Re: your "Is there a better way than renormalization?" post"**Previous message:**Stephen Paul King: "[time 56] Re: Response to comments on "SR as a consequence of a-priori axioms"**Next in thread:**Hitoshi Kitada: "[time 61] RE: [time 57] Re: [time 52] Orientation of time"

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