Subject: Re: Time and its existance
From: tdp@ix.netcom.com(Tom Potter)
Date: 17 Dec 1996 18:01:14 GMT
One body's mass is another body's media ( Time and space ).
This can be expressed as:
mass(A) * G = distance(B)^3
--------------
time(common)^2
mass(B) * G = distance(A)^3
--------------
time(common)^2
Where:
G is the universal gravitational constant,
which does no more than make both sides of
the equation balance. If "G" was set equal to
one, then the units of mass would follow
after the units of time and distance were defined.
Time(common) is the common period ( divided by 2 pi )
shared by interacting bodies. Time is what two interacting
bodies share, and what is unique to each body is their
distance from the common center they share.
Distance(A) and distance(B) are the distances
from each body to the system center of mass.
Classical physics treats distance as the distance
between two bodies, but this introduces an
assymetry and an error which must be corrected
by a "reduced mass" adjustment.
-------------
The distance between two independent intereacting
bodies, or between a body and the center of mass
it shares with another body, can be expressed as:
distance = interaction time * C
Where "C" is the universal distance per interaction time
constant, better known as "the speed of light".
-----------
We can then restate the equations that
express the relationships between two bodies as:
mass(A) * G = ( interaction time(B) * C)^3
-------------------------
time(common)^2
mass(B) * G = ( interaction time(A) * C)^3
----------------------------
time(common)^2
-------------
If we divide both side of the equation by C^3
we get:
mass(A) * G = interaction time(B)^3
----------- -------------------------
C^3 time(common)^2
mass(B) * G = interaction time(A)^3
----------- -------------------------
C^3 time(common)^2
Now, I assert that G / C^3 is nothing more
than a universal time per mass constant,
and that time can be expressed most simply
in terms of a time, and that this time
is a simplier ( and less precise ) expression
of the media that it represents.
In other words, we perceive objects, which
possess the property of mass ( Basically
a composite time property ), as varying in
media composed of time and space ( basically
an interaction time expressed as space to
differentiate it from the common time shared
by interacting bodies ( period time )).
Now, the mass of a body is a simplified,
composite expression of the media of
the body that it is interacting with.
The bottom line is, that media is a
more basis, and more complete definition
of mass, and the most fundamental way to
define both mass and media, is in terms
of the interaction time between a body
and the center it shares with another "body",
and the common time it share with the other body.
The universe is a composite of "standing waves",
and time is the ratio of these waves.
All else, including mass, objects and media, follows from time.
If anyone is interested in a more complete
explanation of this, visit my Web site.
Tom Potter http://pobox.com/~tdp
Subject: This Week's Finds in Mathematical Physics (Week 96)
From: baez@math.ucr.edu (John Baez)
Date: 16 Dec 1996 16:17:30 -0800
This Week's Finds in Mathematical Physics - Week 96
John Baez
Lots of cool papers have been appearing which I've been neglecting
in my attempts to write expository stuff about string theory, lattices,
category theory, and all that. It's time to start catching up!
Let me start with the following book:
1) J. Scott Carter, Daniel E. Flath and Masahico Saito,
"The Classical and Quantum 6j-Symbols", Princeton University
Press, Princeton, 1995. ISBN 0-691-02730-7.
Ever since Jones discovered the Jones polynomial invariant of knots,
an amazing story has been unfolding about the relation between algebra
and 3-dimensional topology. Some key players in this story are the
"quantum groups": certain noncommutative algebras analogous to the
commutative algebras of functions on groups. In fact, not merely
are they analogous, they depend on a parameter, usually called
Planck's constant or hbar, and in the classical limit where hbar -> 0
they actually reduce to algebras of functions on familiar groups. The
simplest case is "quantum SU(2)", which reduces in the classical
limit to the group SU(2) of 2x2 unitary matrices with determinant 1.
Ironically, it's good old "classical SU(2)" that governs the quantum
mechanical theory of angular momentum. Quantum SU(2) was first
discovered by people working on physics in 2-dimensional spacetime,
where when you quantize certain systems you also need to quantize their
group of symmetries!
Nowadays, mathematicians find it simpler to work with the closely
related "quantum SL(2)", a quantization of the the group SL(2)
of all 2x2 complex matrices with determinant 1. The above book is
largely about quantum SL(2) and its applications to topology.
All quantum groups give rise to invariants of knots, links, and
tangles. They also give rise to 3-dimensional topological quantum
field theories of "Turaev-Viro type". This is a kind of quantum field
theory you can define on a 3-dimensional spacetime that you've triangulated,
i.e., chopped up into tetrahedra. One of the main things you want to
compute in a quantum field theory is the "partition function", and we say
the Turaev-Viro theories are "topological" because you get the same answer
for the partition function no matter how you triangulate the 3-dimensional
manifold corresponding to your spacetime: the partition function only
depends on the topology of the manifold. The SU(2) Turaev-Viro theory,
the first one to be discovered, is also one of the most interesting because,
modulo a few subtle points, this theory is just quantum gravity in
3 dimensions (see "week16"). The basic idea, though, is that you compute
the partition function by summing over all ways of labelling the edges of
your tetrahedra by "spins" j = 0, 1/2, 1, 3/2, etc.. Ponzano and Regge
had tried to set up 3-dimensional quantum gravity this way previously,
but there were problems getting the sum to converge. The neat thing about
the quantum group is that you only sum over spins less than some fixed spin
depending on the value of hbar. Since the sums are finite, they automatically
converge.
It turns out that in these Turaev-Viro theories you are not actually
taking advantage of all the structure of the quantum group. Using the
extra structure, you can also use quantum groups to define certain
*4-dimensional* topological quantum field theories, those of
"Crane-Yetter-Broda" type. Here you triangulate a 4-dimensional manifold
and, in the SU(2) case, you label both the 2d faces the 3d tetrahedra with
spins. Actually, lots of people think the Crane-Yetter-Broda theories are
boring, because they look sort of boring if you only examine their
implications for 4-dimensional topology. However, they become interesting
when you realize that, like all topological quantum field theories defined
using triangulations, they are "extended topological quantum field theories".
Roughly speaking this means that they have implications for all
dimensions below the dimension they live in.
In particular, the Crane-Yetter-Broda theories spawn 3-dimensional
topological quantum field theories of "Chern-Simons-Reshetikhin-Turaev"
type, and most people agree that *these* are interesting. I like to
emphasize, however, that a deep understanding of these 3-dimensional
progeny requires an understanding of their seemingly innocuous 4-dimensional
ancestors. Also, there are a lot of interesting relationships between
the SU(2) Crane-Yetter-Broda model and quantum gravity in 4 dimensions, which
we are just beginning to understand. See "week56" for a bit about this.
If you haven't yet joined the fun, Carter, Saito, and Flath's book is a
great place to start learning about the marvelous interplay between
algebra, topology, and physics in 3 and 4 dimensions. Needless to say,
it doesn't cover all the ground I've sketched above. Instead, it focuses
on a rather specific and concrete aspect: the 6j symbols. This should
make it especially handy for beginners who aren't familiar with category
theory, path integrals, and all that jazz.
What are the 6j symbols, anyway? Here I need to get a wee bit more technical.
The "classical" 6j symbols are important in the representation theory of
plain old classical SU(2), while the "quantum" ones are analogous gadgets
applicable to quantum SU(2). In either case the idea is the same. SU(2),
classical or quantum, has different representations corresponding to different
spins j = 0, 1/2, 1, 3/2, etc.. (If you don't know what I mean by this, try
"week5".) If we take three representations j1, j2, and j3, we can tensor
them either like this:
(j1 tensor j2) tensor j3
or like this
j1 tensor (j2 tensor j3)
The tensor product is associative, but that doesn't mean that the
above two representations are *equal*. They are only *isomorphic*.
This *isomorphism* can be thought of as just a big fat matrix, and
the entries in this matrix are a bunch of numbers, the 6j symbols.
Turaev and Viro used the quantum 6j symbols to define the original
Turaev-Viro model. It goes like this: first you chop your 3-dimensional
manifold up into tetrahedra, and then you consider all possible ways
of labelling the edges with spins. Each tetrahedron gets labelled with
6 spins since it has 6 edges, and from these spins we can compute a
number: the 6j symbol. Then we multiply all these together, one for each
tetrahedron, and finally we sum over labellings to get the partition function.
Marvelously, the identities satisfied by the 6j symbols are precisely what's
needed to make the result independent of the triangulation! See "week38" for
an explanation of this seeming miracle: it's actually no miracle at all.
2) E. Guadagnini, L. Pilo, Three-manifold invariants and their relation
with the fundamental group, 22 pages in LaTeX available as hep-th/9612090.
Fans of topological field theory may like this one, though I must
admit I haven't gotten around to doing more than reading the abstract
yet. In this paper the authors give evidence for the conjecture
that among 3-manifolds M for which the Chern-Simons invariant CS(M) is
nonzero, the absolute value |CS(M)| only depends on the fundamental
group of M. Chern-Simons theory depends on a choice of group; they
prove the conjecture for certain manifolds ("lens spaces") when
the group is SU(2), and give numerical evidence when the gauge group
is SU(3).
What's interesting about this to me is that |CS(M)|^2 is just the
Turaev-Viro theory partition function, so this conjecture is saying
that the Turaev-Viro theories discussed above have a tendency to notice
only the fundamental group.
3) Michael Reisenberger and Carlo Rovelli, "Sum over surfaces" form
of loop quantum gravity, preprint available as gr-qc/9612035.
This wonderful paper should really push forwards our understanding
of the loop representation of quantum gravity. I talked a little
bit about the basic idea in "week86". In the loop representation,
a state of quantum gravity at a given moment is represented by a bunch
of knotted loops or "spin networks" in space. What's the spacetime
picture? Well, if you have a surface in spacetime and look at it
at one moment of time, it typically looks like a bunch of loops... so
maybe the spacetime picture of quantum gravity is that spacetime is
packed with 2-dimensional surfaces, all tangled up. Interestingly,
this is also very reminiscent of the picture of quantum gravity in
string theory!
I've been working on this sort of idea ever since I wrote a paper
suggesting that the loop representation and string theory might be
two faces of the same ideas (see "week18"). Since then, most of the
time I've been trying to understand how these ideas relate to the
Crane-Yetter-Broda theories, and trying to set up the necessary *algebra*
(n-category theory) to deal nicely with surfaces in 4-dimensional spacetime.
But there are many other angles from which one can attack this problem,
and one of the best is to start directly from Einstein's equations
for general relativity, try to quantize them using the path-integral
approach, and see how the path integral can be written as a sum over
surfaces. Reisenberger has already begun work on this in the context of
"simplicial quantum gravity" - where you chop spacetime up into
the 4-dimensional analog of tetrahedra. But during the Vienna workshop
on canonical quantum gravity this summer, we talked about a different,
still more direct approach (see "week89"). The idea is to copy standard
quantum field theory, write the propagator describing time evolution
as a time-ordered exponential, and interpret the terms in the resulting
sum as surfaces in spacetime. It's all very analogous to traditional
Feynman diagrams, where you write the propagator as a sum over diagrams,
but now the "Feynman diagrams" are 2-dimensional surfaces. (Again, this
is reminiscent of string theory - but with many important differences.)
There is much more to say, but I think I'll leave it at that....
Over in the world of n-categories there is also some very interesting
stuff happening, which I will discuss more next week. I'm almost done
writing a paper with James Dolan on the definition of n-categories, but
in the meantime some other folks have been coming up with other definitions of
n-categories, so we will soon be in the position to compare definitions and
see how similar or different they are, and start erecting the formalism
needed to deal with all these topological quantum field theories and
"sums over surfaces" in a really elegant way! Everything looks like its
fitting together. At least, that's my momentary optimistic feeling.
Perhaps it's just the fact that classes are over that is making me so happy.
Yes, it's probably just that.
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained by anonymous ftp from math.ucr.edu; they are in the
subdirectory pub/baez. The README file lists the contents of all the
papers. On the World-Wide Web, you can get these files by going to
http://math.ucr.edu/home/baez/
A complete index of the old issues of "This Week's Finds" is available
at
http://math.ucr.edu/home/baez/twf.html
but if you are cursed with a slow connection and just want a jumping-off
place to the olds issues, go to
http://math.ucr.edu/home/baez/twfshort.html
For the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
Subject: Re: NASA lies, again.
From: singtech@teleport.com (Charles Cagle)
Date: Tue, 17 Dec 1996 13:51:08 -0800
In article <32b2bc70.2511968899@news.smart.net>, stephani@smart.net wrote:
that C. Cagle had written:
>>There you go; admitting freely that your choice of friends includes a
>>number of 'Welfare Queens in White Coats'.
>
>I just wonder if you have a point here, or if you're parroting some
>party line or talk show host. It's clear you don't know any
>government employees; it's also clear that you are uninterested in the
>facts, except where they back up your hastily-formed opinion.
Your half witted response indicates that it is you that has little
interest in the facts. I know lots of gov't employees. And my opinion,
oh swami know it all who knows nothing, has taken nigh on fifty years to
form. Perhaps that's 'hastiness' where you come from.
>>
>>> Like all other human beings, some government workers are
>>>worth their pay, some are not, and some don't get paid nearly enough for
>>>what they do. There are some really good people working for the
>>>government who could make quite a bit more money working in the private
>>>sector, but who choose public service.
>>
>>Probably because its easier.
>
>I work for the government. I've done the private sector thing too,
And probably couldn't cut it in the real world.
>and I recognize that there are some people in the private sector who
>work very hard indeed.
No doubt why you couldn't make it.
>But the job I have now takes more of my time
>and energy than anything else I've attempted to do, graduate school
>included.
Probably because you are utterly incompetent at what you do. Most likely
you are a personification of the Peter Principle. The fact that you are
'attempting' to do your job says it all.
>>
>>> It really pisses me off when some
>>>jerk mouths off about how evil (or lazy, inefficient, etc.) the government
>>>and government workers are without having any real evidence to back it up.
>>
>>I wonder who programmed that into your head? Couldn't be you, right? So,
>>you get pissed off do you when someone 'pushes your button' by conforming
>>to a set of parameters which you yourself have set up? Exactly whose
>>problem to do suppose that is? And you refer to others as 'jerks'? :-)
>>
>>As far as evidence to back it up...wow! What a laugh! There's
>>practically nothing but evidence. If we could just put the armor plating
>>that you apparently have on your head on our Army tanks why we would be
>>invincible. :-).
>
>Okay, so, where is this evidence? The fact that some departments in
>government have been inefficient in spending the taxpayers' money
>(something I will not gainsay) does not mean that government workers
>are lazy.
Just cowards who will not stand up and make a fuss about the waste and
theft. But why should they? Because they are without honor and will
stand by and allow theft and incompetence to reign because it is from such
they gain their own sustenance.
> You are stating that anyone who works for the government
>must _on that account_, be lazy, ineffectual, or stupid.
I didn't use those terms, but now that you've put it like that...Because
you haven't seen it can only mean you are too *lazy* to look for it, too
*ineffectual* to find it, and too *stupid* to recognize it when you are
immersed head first in it.
>I've seen no
>evidence of that, even in the tattier publications; I have seen
>opinions (like yours) put forth without evidence. I'm still waiting
>for that evidence.
Likely, you, being blind to your own incompetence, will never recognize
the evidence.
>>>People are people. Even government workers.
>>
>>Gee and I thought gov't workers were parasites. You learn something
every day.
>
>Name-calling makes you look foolish.
While attempting to defend the indefensible merely establishes your
blindness and lack of conscience.
--
C. Cagle
SingTech
Subject: Re: NASA lies, again.
From: singtech@teleport.com (Charles Cagle)
Date: Tue, 17 Dec 1996 14:12:35 -0800
In article <58uu92$cao@trojan.neta.com>, blair@trojan.neta.com (Blair P
Houghton) wrote:
>Charles Cagle wrote:
>>jwalters@clark.net (Jim Walters) wrote:
>>>By the way, I don't work for NASA. However I have lived within commuting
>>>distance of Washington, DC for almost seven years now, and a lot of my
>>>friends and acquaintances are US government employees. Some of them even
>>>work for NASA.
>>
>>There you go; admitting freely that your choice of friends includes a
>>number of 'Welfare Queens in White Coats'.
>
>Y'know, applying that sort of insult to some of the most
>intelligent and productive people ever to grace human
>history makes you look like a complete idiot.
And your defense of those people establishes that you are without moral
conscience.
>>>There are some really good people working for the
>>>government who could make quite a bit more money working in the private
>>>sector, but who choose public service.
>>
>>Probably because its easier.
>
>Almost always because it's challenging and satisfying. I
>happen to work in a place where there are a surprising
>number of former NASA engineers, whether employees or
>subcontractors, and the reason they give most for leaving
>NASA is that the private-sector money for their skills is
>far too large to turn down.
Most likely the place you work is sucking the gov't tit. So they changed
jobs because the money was better. Shows you they weren't so dedicated
after all but merely intellectual whores such as yourself.
>>> It really pisses me off when some
>>>jerk mouths off about how evil (or lazy, inefficient, etc.) the government
>>>and government workers are without having any real evidence to back it up.
>>
>>I wonder who programmed that into your head? Couldn't be you, right?
>
>And perhaps you can tell us who programmed your irrational
>anti-government-worker prejudice into your head?
>
>>So, you get pissed off do you when someone 'pushes your button' by conforming
>>to a set of parameters which you yourself have set up?
>
>So you don't like it when someone recognizes that you're
>being a jerk?
>
>The attitude you displayed was tantamount to a troll for
>people on this net who would disagree with you;
That's right and you slack jawed bottom feed, you took the bait, didn't you?
>especially
>considering that the attitude is abhorrent and almost
>anyone (except maybe Randy Weaver) could find it in
>themselves to disagree with you.
You lockstepp moron. You think what the Gov't did to Weaver was right?
If so, may they do the same to you and your family.
>Jim was in fact expressing what amounts to the community
>standard, and I'm confident the community applauded it.
Hey, Mr. herd instinct....is that how you do science and form your
opinions? By consensus?
>>Exactly whose problem to do suppose that is?
>
>Apparently it's yours. He's got a valid point and you're
>a prejudiced jerk.
>
>>And you refer to others as 'jerks'? :-)
>
>Sounds like he knows one when he sees one, jerk.
This is fun, playing you along. Seeing you make your incompetent runs and
trying to get off the hook, but the hook is set and you are the fish. Too
bad you aren't fit for anything but fertilizer.
>>As far as evidence to back it up...wow! What a laugh! There's
>>practically nothing but evidence.
>
>"Practically nothing but evidence." That's not evidence.
>And anecdotes won't do, either. You made a generalization
>about everyone who works for NASA and you'll either have to
>back that up or eat the crow you're roasting for yourself.
>Silence or evasion will of course be inferred to agree that
>you're a coward and a liar.
What, and join company with you? Never!
>>>People are people. Even government workers.
>>
>>Gee and I thought gov't workers were parasites. You learn something
every day.
>
>Today we learned that Charles Cagle is an abusive and irrational
>loser who has nothing better to do than insult his betters.
>
> --Blair
> "You jerk."
And we learned that Blair P Houghton considers himself the better of all
who know of his utter incompetence and dishonestly and inability to
demonstrate rationality
