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

*Mon, 07 Jun 1999 14:16:44 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 394] Re: [time 391] Re: [time 388] Re: [time 384] Re: [time 380] Re: [time 376] Whatare observers"**Previous message:**Matti Pitkanen: "[time 392] Information and information gain of conscious experience"**Next in thread:**Matti Pitkanen: "[time 395] Re: Constructing space-times"

Dear Matti,

I am reminded of an on-going conversation that my off-line friend Paul

Hanna and I have been having concerning how to generalize the definition

of velocity (and motions of "particles" in general) into the language of

probabilities. My ideas here are very rough so I beg for your patience

and critique. In [time 392] you said:

[MP]

"In quantum field theory situation is different since it is not possible

to interpret time evolution as evolution in any kind of configuration

space (the required assignment of the space of quantum states to single

point of 3-space does not make sense). Problems are also caused by the

fact that probability density is not scalar quantity anymore but time

component of a 4-vector."

[SPK]

Could we not see this as a problem and consider its implications? If

the probability density is the time component of a 4-vector, what would

the spatial components be?

and:

[MP]

"b) One can also worry about General Coordinate Invariance.

In case of a nonrelativistic Schroedinger equation the information

is Galilei invariant. In case of QFT Lorentz invariance

is lost since probability density behaves like a component

of a four-vector."

[SPK]

Can we construct a Lorentz group for the 4-vector of a single particle

(as an observer), such that it would have an *illusion* of a preferred

inertial frame? Thus a *space-time* is identified with the range of

possible states (wrong word!) of the group and such for any particle. We

modify this construction to account for the space-times of different

types of particles, e.g. photons, neutrinos, electrons, etc.

I effectively reversing the usual way that physics is done, instead of

assuming an a priori space-time and then figuring out the group

theoretic behaviors of objects "in it", I am saying that we consider the

group theoretic properties of a particle as defining, a postiori, the

particular space-time that it would have. Does this make any sense?

and further:

[MP]

"One is accustomed to speak about communication as information flow.

Therefore one could wonder whether it is possible to define the concept

of information current somehow in quantum TGD framework.

U_a, a-->infty is indeed defined as a time evolution operator associated

with Virasoro generator L_0 playing the role of Hamiltonian.

Hence it should be possible to formally associate with

the time evolution U_a a conserved probability current having time

component I^a plus spatial components in the degrees of

freedom characterized by the coordinates of the reduced configuration

space. This assignment would be completely analogous to that performed

for

the ordinary Schroedinger equation and the Lorentz invariance of

the lightcone proper time coordinate a would make this assignment

possible."

[SPK]

Could we think of this U_a as identified with individual LSs, such that

it would represent the "perceived" space-time and act as the external

counterpart to the internal unitary propagator group that defines the

LSs internal clock. This notion would make explicit the subject-object

duality existing between each LS and its set of observables.

[MP]

"In p-adic context n= Log_pR is pseudo constant

for finite values of the integer n and this would mean

that information current would be conserved locally in p-adic sense.

This would *not* imply the conservation of information even

in the case that n is pseudo constant everywhere.

[SPK]

This "everywhere" is not absolute, but bounded relative to a given p?

Thus we do not have a unitarity violation problem when changing

framings[1], since each framing (defined as a p-adic space-time patch)

would have its own convex set of information that is "conserved".

[1] This "framing" notion relates to how the composition of an LS is

altered when we shift between perspectives, like the situation discussed

by Hitoshi in Section 9 of http://www.kitada.com/bin/time_I.pdf and what

I understand of your discussion of biological p-adic physics [time 377]

etc.

[MP]

If this indeed works, one could assign

with a given time evolution U_a transfer of information in

the reduced configuration space of 3-surfaces. The zero modes

characterizing the nondeterminism of the K\"ahler action

contain information about the moments for multifurcations in the

time development of the spacetime surface and this

gives hopes of approximate reduction of this

information flow to an effective information flow

occurring at the level of 'quantum average effective spacetime'."

[SPK]

I am thinking of the motions of "particles" (consistent with Hitoshi's

center-of-mass definition of the exteriors of LSs) as being modelable,

in a fundamental sense, by a "probability density current" quantity.

It is "probabilistic" since its possible directions are not a priori

definite but are defined by the observational act, which is an

interaction subject to finite constraints between pairs of LSs. It is a

"density" because it is a quantity that is not a priori single valued

nor a priori localized to a single point, and a "current" because there

is a continuous "flow" to the individual components due to the existence

of a potential, which I think exists due to the non-absoluteness of the

optimization. We can see that if the potential vanishes, so does the

possibility of a change in the velocity and the information is identical

everywhere in the U^T (this is another way of saying that U^T is a bound

state and is at absolute equilibrium with all proper subsets of itself).

Perhaps these notion is nonsensical! :) I am just trying to work out

how it is that we observe an illusion of continuous motions and can

communicate about these to each other when we can prove that they are

not real, e.g. they are an illusion! :)

see:

http://lobelia.physics.wisc.edu/duncan/phys531/wavemechanics/node2.html

Onwards to the Unknown,

Stephen

**Next message:**Hitoshi Kitada: "[time 394] Re: [time 391] Re: [time 388] Re: [time 384] Re: [time 380] Re: [time 376] Whatare observers"**Previous message:**Matti Pitkanen: "[time 392] Information and information gain of conscious experience"**Next in thread:**Matti Pitkanen: "[time 395] Re: Constructing space-times"

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