test

[Ken S. Tucker]

From SPF....

Hi Neurop, Jay and all.

On Jul 22, 9:35 pm, neurop...@yahoo.com.au wrote:
> Jay Yablon wrote:
>
> > I started a Wiki article on this (not your spanking fetish,
> > but FW) at:
> >
> >http://en.wikipedia.org/wiki/Foldy-Wouthuysen_transformation
>
> OMG! I must have left some acid lying around and you tried it.
> (I know I've got enough cheek to fill the Grand Canyon, but
> I wouldn't even dream of writing a Wiki article at my
> present state of knowledge.)

My problem with Jay's F-W article is, if it is Generally Covariant,
it appears to me the whole problem exists in the Twilight Zone,
where GC is concerned.
((Neurop, I respect your ref's, I'm researching back to my 1932
text entitled, "The Elements of the New Quantum Mechanics"
(Halpern & Thirring), to DeBroglie's foundation)).
DeBroglie into the "phase wave" for relativistic purposes that
are somewhat unclear to me, that I post on later.
Regards
Ken S. Tucker
[snip good stuff]

[Ken S. Tucker]

On Jul 23, 7:20 pm, neurop...@yahoo.com.au wrote:

> On Jul 24, 5:08 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > Hi Neurop, Jay and all.
>

> Hi Kenny-Boy! (Oh goodie - another playmate! That'll be more fun.
> Which way do you like it?)

I'm a student, mainly lurking this subject.

> > My problem with Jay's F-W article is, if it is Generally Covariant,
> > it appears to me the whole problem exists in the Twilight Zone,
> > where GC is concerned.
>

> But isn't this stuff all about special-relativistic theories?

To start yes, but SR is restricted relativity. The positive and
negative energy solutions (Dirac's) all need to obey GR's
Principle of Equivalence, IOW's negative energy does not
fall up.
((I think that's referred to a the "hole creation operator"))

Secondly, any physical laws in the F-W representation are
true in all CS's even those that accelerate, and thus need
a clear *tensorial* description.

> The FW transformation is a canonical transformation of a
> Poincare-invariant theory. Not sure what GC has to do with it.

IMHO, if position is relative, then it's derivative (speed) is
relative (SR) and it's derivative (acceleration) is relative (GR)
and so forth finally ending up with GC.

> (Though of course, CT's in the dynamical group get a bit
> tricky when you're mixing positions and momenta.)

Usually I fall back on a cheap Curl like,

(X^u / r) U^v - (X^v / r) U^u

which is quantized.
I wonder if the quantization of charge and spin are relatable
at a more fundamental level !?!.

> > ((Neurop, I respect your ref's, [...]
>
> Oh, don't respect me *too* much! That's no fun.

Well you got me hunting back to 1932!

> LOL from the Princess(es)!

Regards
Ken S. Tucker
(aka Rachel)

BTW: Do know how McAnally's doing?

[Ken S. Tucker]

Hi Jay, thank you for the link.

On Jul 25, 8:57 pm, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:
> The last thread has become rather large, so I will regroup and pick up
> the discussion here. I have also, for solely academic, non-commercial
> purposes, posted the original FW paper here:
>
> http://jayryablon.files.wordpress.com/2008/07/foldy-wouthuysen-origin...
>
> so that others who are interested may study this as well. This will
> remain posted for a limited time -- about ten days.
>
> Anyway, I will retreat from the notion that I have corrected a
> long-standing error in NW, to trying to straighten out what Princess
> Neuropulp and I have agreed are some "misnomers" in the original paper,
> particularly as regards so-called "mean" operators which have nothing to
> do with expectation values in the sense of a scalar statistical
> observable <psi|O|psi>.
>
> If you go to Table 1 of the FW paper, there are four velocity operators
> in total, two for the "old" Dirac-Pauli representation, and two for the
> "new" FW representation.
>
> If one carries out the calculation of commuting the Hamiltonian with the
> canonical position, i.e., if one calculates out [H,x], and if the
> unitary FW operator is U, and if:
>
> H' = U H U^-1
> x' = U x U^-1
>
> then there are four combinations of H and x leading to four different
> operators which corresponded to the velocity operators in Table 1:
>
> i[H,x] = \alpha ("Velocity" in "old" rep)
> i[H',x] = \beta p / E_p ("Mean velocity" in "new" rep.)
> i[H',x'] = \alpha + . . . ("Velocity" in "new" rep)
> i[H,x'] = p/E_p (...) ("Mean velocity" in "old" rep.)
>
> So, I'll pose the problem of trying to gain a sensible physical
> perspective on the meaning of each of these velocity operators, which
> presumably can be carried over to other operators as well.
>
> I will start by noting that when one takes i[H,x], one is arriving at
> dx/dt, that is, H, when commuted with O, essentially yields dO/dt. It
> is H with plays the role of the 1/dt operation (nothing new).
>
> But this means that if we connect the above to the effective time
> differentiation that arises from canonical commutation with H, we would
> have:
>
> dx/dt=i[H,x] = \alpha ("Velocity" in "old" rep)
> dx/dt'=i[H',x] = \beta p / E_p ("Mean velocity" in "new" rep.)
> dx'/dt'=i[H',x'] = \alpha + . . . ("Velocity" in "new" rep)
> dx'/dt=i[H,x'] = p/E_p (...) ("Mean velocity" in "old" rep.)
>
> So, what are these operations really telling us, physically? It seems
> to me that we need to be considering that we are effectively engaging in
> a transformation of *time* for two of these four operations. This leads
> to some interesting considerations on three fronts: a) canonical
> transformations are applied to position, but here we need to consider
> those which involve time b) we have position operators but perhaps we
> should be considering time operators also, and c) we need overall to
> consider Lorentz covariance properties, which brings me to my pet peeve
> about time parameter defined in each individual observer's "personal
> space." Just thinking out loud for right now.
> Further insights, please?

Eq.(34) looks somewhat behaved. I reworked it in tensors to,

H^u = g^uv P_v - e A^u , Eq.(34ken)

g^00 == BETA , g^0i == ALPHA ,

At this point I sub in MST
http://physics.trak4.com/modern-spacetime.pdf

P_0 = rest mass, P_i=0,

H^0 = g^00 P_0 - e A^0 .

Now we may set H^0 = 0 to obtain,

P_0 = e A_0

to provide the "electrostatic potential energy" of
charge "e" in potential "A_0", as the constituences
of the electron within it's structure using a summation,
(A_0 = A),

P_0 = SIGMA (over i,j (i=/=j)), e(i) A(j)..../c^2

To obtain the electron mass, the minimum summation
of i,j I find is 3.
____________________________
> Jay R. Yablon
> Email: jyab...@nycap.rr.com
> co-moderator: sci.physics.foundations
> Weblog:http://jayryablon.wordpress.com/
> Web Site:http://home.nycap.rr.com/jry/FermionMass.htm

Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Jay and all.

On Jul 26, 11:20 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
> Hi Jay, thank you for the link.
>
> On Jul 25, 8:57 pm, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:

...
> >http://jayryablon.files.wordpress.com/2008/07/foldy-wouthuysen-origin...
...

> > Further insights, please?
>
> Eq.(34) looks somewhat behaved. I reworked it in tensors to,
>
> H^u = g^uv P_v - e A^u , Eq.(34ken)
>
> g^00 == BETA , g^0i == ALPHA ,
>

> At this point I sub in MSThttp://physics.trak4.com/modern-spacetime.pdf

>
> P_0 = rest mass, P_i=0,
>
> H^0 = g^00 P_0 - e A^0 .
>
> Now we may set H^0 = 0 to obtain,
>
> P_0 = e A_0
>
> to provide the "electrostatic potential energy" of
> charge "e" in potential "A_0", as the constituences
> of the electron within it's structure using a summation,
> (A_0 = A),
>
> P_0 = SIGMA (over i,j (i=/=j)), e(i) A(j)..../c^2
>
> To obtain the electron mass, the minimum summation
> of i,j I find is 3.

> Ken

The Eq.(34ken) above appears to be ok, ((though
it could be a bastardization)).
If so, then that covariant expression confers advantages.

1st I tested the equation by *assuming* a CS exists
allowing me to set H^0=0 in that CS, and see if the
result was reasonable, I think the resulting
P_0 = e A_0 is ok physically, and can be interpreted
as the inertia of the charge "e" is in proportion to the
potential A_0.

If I were to generalize Eq.(34ken) further by setting
H^u =0 then,

e A^u = g^uv P_v == P^u

It's sloppy to self energize a charge in it's own potential,
so let's define A^u as the effecting potential on charge "a"
due to charge "b" (we can do a large summation of effecting
charges, but one is a good start) and write,

P^u (a) = a A^u

and likewise

P^u (b) = b B^u

From those we can define the invariant P^2 = P_u P^u
with more precision,

P^2 (a,b) = P^u(a) * P_u(b)

= a*(b/s) * b*(a/s)

where "s" separates charges "a" and "b", giving

P =a*b/s

as the invariant mass.

I should mention, I/we used that definition of invariant
mass (energy) applied to General Relativity,
http://physics.trak4.com/GR_Charge_Couple.pdf
and it provides an elementary solution.
Regards
Ken S. Tucker

[Ken S. Tucker]

I think what Princess did is to expound in her own way
a frustration, about requiring a continuum for a derivative,
when the problem is dX = 0 and X <> constant, and our
old differential calculus does NOT apply.
Mathematical techniques have a domain of appliance.

In physics we say Power = dEnergy/dTime = Watts,
but in the Quantum realm, when I switch on a 60 watt
light bulb, *photons* are emitted, and there is no such
thing as a derivative of a photon.

The bulb is actually doing DE/DT , (D is increment),
and the summation of Energy is E=DE1+DE2+DE3...
where the DE's are transfered via photons of various
energies. Since the derivative d(DE)=0, it follows the
derivative dE=0.

The differential calculus was invented to apply to
macroscopic bodies, especially astronomical and
then gradually was successfully applied to many
other fields, where a *continuum* can be *assumed*

I think it's important to understand that Power which
by another name is the "flow of energy", is quantized
just as the flow of current - either electrical, or a fluid,
is also quantized.

It appears to me, physicists are racking their brains
out to merge differential calculus and Quantum Theory,
but what if that's not possible?
That problem reminds me of trying to trisect an angle,
using a ruler and compass, and I'm still trying in spite
of Gauss proving it cannot be done.

So we need to prove differential calculus and QT can
merge, to make sense of,
dX = 0 and X <> constant

Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Neurop and fella's,
I studied all the posts to this time.

> Sir Kenneth wrote:

You can call me Tucker.

> > I think what Princess did is to expound in her own way a
> > frustration, about requiring a continuum for a derivative,
> > when the problem is dX = 0 and X <> constant, and our old

> > differential calculus does NOT apply. ....
>
> Well, no, not really. That's not what I was doing. I was
> trying to explain to Sir Jay how the notion of derivative
> can indeed continue to make sense in the context of a
> noncommutative algebra of quantum operators.

>
> > It appears to me, physicists are racking their brains out to
> > merge differential calculus and Quantum Theory, but what if
> > that's not possible?

> There are plenty more arcane ways to attack such things.
> (Topological QFT comes to mind.) Much of theoretical physics
> can be recast in terms of Lie algebras (or rather,
> Lie-Poisson algebras) where you start with a non-commutative
> Lie algebra, and construct a Poisson representation. A
> Poisson algebra is basically a Lie algebra that is also a
> "derivation" (meaning that the Lie product also obeys the
> Leibniz rule). The interesting ones tend to be infinite
> dimensional function spaces.

My problem with "infinite...spaces" is that we eventually
must return to 4D + an event sequence to provide a
measureable prediction. I have a "particle accelerator"
sitting on my bench here, aka an oscilloscope.

> You can go a very long way with that sort of toolkit. From
> classical mechanics, to quantum theory, and even to
> non-equilibrium quantum thermodynamics (though I don't know
> too much about the latter). The important bit is that the
> algebras and their representations be amenable to analysis
> (in the rigorous mathematical sense of that word). That
> means we need to make sure we're dealing with
> topological spaces satisfying certain additional axioms
> concerning "separation" and "countability" (and a few
> others) which I'll skip for now.

ok.

> Certain hard problems at the frontiers of physics research
> revolve around topological issues. Eg, non-countability of
> the state spaces in quantum gravity, and those pesky
> divergences and anomalies in field theory that basically
> come from sloppy handling of topological details about how
> the operator algebras and their duals (state spaces) fit
> together.

ok.

> > So we need to prove differential calculus and QT can merge,
>

> It's not so much differential calculus and QT", but rather
> "finding appropriate topologies and algebras that solve
> current theoretical physics issues rigorously."

Perhaps you would enjoy a High School level problem,
in QFT.
Let "a" and "b" be two separate charges.
Let E(b) = b/r^2 be the Electric field of "b".
The standard electrostatic force is F(a,b) = a*E(b) or
F(b,a)= b*E(a), and an asymmetry developes where
F(a,b)=-F(b,a) cuz the Force vectors are relatively
opposite depending on position, with magnitude,

F=a*b/r^2.

with "total system electrostatic energy" "U" being,

U= a*b/r

and we quantize the E-field by,

a*b = F*r^2,

where "a*b" can be regarded as in dimensions of
area or Planck's "h", (action or angular momentum),
either way the *fundamental charge* and h are finite
*quantized* invariants.

If you are now provided with the EM field tensor F_uv
how would you explain the above?

> (Ah, that feels better now. I needed that.)

Me too, I'm often frustrated.

> LOL from (some of) the Princesses!
> (You haven't met them all yet. I think Princess Leather-Bottom
> might need to make an appearance soon. She likes being spanked.)

LOL. We crafted our SPF charter without regard to
consideration of sexy stuff, IOW's we have no policy
on that stuff. However I'll vouch for Princess Leather-
Bottom by stating it is a Fundamental biological fact
that 1+1 + 9 months can be greater than 2, presuming
life is quantized...I'll defer to Mr. Yablon on that.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Ah Ha and all.

On Jul 31, 9:26 pm, Ah Ha <ProfHarri...@gmail.com> wrote:
> On Jul 31, 2:11 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:

> > > So I have a question for this group. What would a unification of
> > > differential calculus and quantum theory entail? What if the
> > > differential calculus made equal sense for both large macroscopic
> > > bodies and "infinitesimals" and fit within the framework of standard
> > > analysis (as opposed to nonstandard analysis)? Do you have a wish
> > > list for such a calculus to shed light on QT?
> > > Would "differentiating
> > > photons" be on the list as something important and vital?

Still pondering those questions.

> > dX=0 , X=/=0 , X is not equal to zero.
>
> Ah, this is something I have thought about. Are you familiar with
> Hassler Whitney's paper, "A function not constant on a connected set
> of critical points"?

I am now!

> He came up with a function f:R^2 -->R which is
> continuously differentiable and has a connected path of critical
> points, but f is increasing along the path. The path has to be
> nonsmooth, of course, otherwise the fundamental theorem of calculus
> would be contradicted. However, if your function is smoother than the
> path is rough (you can use Hausdorff dimension to make this precise),
> then the function must be constant along the path.

That reminds me of a wheel rolling on a rough surface.
As the wheel shrinks, singularities can be encountered,
but expanding the wheel large enough and they vanish.
I can work that analogy of continuum and quantum, if
it's ok with you.
(Some of my personal research involves Fractional
Calculus, Fractional Interdimensional Transformations,
Asymmetrical Metrics, Dynamic Metric Tensors, and
Tensor Calculus with minimum lengths and Modern
SpaceTime).

> > I'm defining a staircase function, and I'm aware that a
> > Fourier series will describe it, *IFF* an infinite frequency
> > is permitted. I understand that infinite frequency tends
> > to a zero amplitude, so it somehow rationalizes.
> > But here's the big BUTT, scientific method requires
> > proof, and then we get back to the "derivative of a
> > photon", and then HU blows up.
> > (HU is Hiesenberg Uncertainty).
>
> Language may be a problem here. I am the purist kind of mathematician
> and you seem to be using engineering/applied math shorthand.

Understood, I keep one foot in physics, one foot in math,
and too often one foot in my mouth, let me try to be more
pure.
Planck gave birth to Quantum Theory by taking the limit
h => constant INSTEAD of h=>0.

Suppose we compare that to a differential coefficient,
dx/dt=0 to an incremental DX/DT =/=0, where we'll
*assume* x=X and t=T to start. The question is,
is the process of taking the "limit" an issue or is the
assumption x=X, t=T faulty?

The test is to write the equation of a "staircase".

> One day
> it might be worthwhile to stand in front of a blackboard with you and
> sort out what each of us is saying. I am not used to public forums,
> though, especially for brainstorming.

Great, I'm just North of you in Okenagan Valley BC.
and have enjoyed camping beside the Pacific off Hwy(1),
in Calf. and want to do it again, so if you have time we
can meet, also if you happen to be in the area, stop in,
we have plenty of windows and mirrors and eraseable
pens.
Thanks and Regards
Ken S. Tucker
...

[Ken S. Tucker]

Hi Princess

On Jul 31, 9:33 pm, neurop...@yahoo.com.au wrote:

> Ken S. Tucker wrote:
> >> Sir Kenneth wrote:
> > You can call me Tucker.
>

> Oh? Very well. But... plain "Tucker" seems rather naked
> without a respectful title. "Sir Tucker"? Hmmm, no. And
> "Marquis de Tucker" doesn't quite roll off the tongue.
> I'll have to give it more thought.

My lab pals called me Katy, (from KT).

> > My problem with "infinite...spaces" is that we eventually
> > must return to 4D + an event sequence to provide a
> > measureable prediction. I have a "particle accelerator"
> > sitting on my bench here, aka an oscilloscope.
>

> Classical (nonrelativistic) mechanics is already based (in
> general) on infinite dimensional function spaces that (in
> the simplest case) consist of functions of 7 variables (3
> position, 3-momentum, and time). Yes, one must somehow
> extract a simple number out of this to get an experimental
> prediction. That's where the notion of dual spaces comes in.
> An element of the dual is essentially just a linear mapping
> from an element of the primal space of observables to a
> scalar (real or complex), or maybe a simple tuple of scalars
> in the case of vector-valued observable.

What bothers me is the semantics of "degrees of freedom"
being equated to "dimension". The distinction is vital when
Dimensional Analysis is being done.

> But to obtain such simple numbers which can usefully be
> compared with experiment typically requires some form of
> integration over the underlying infinite dimensional space.
> A common example in QFT is the Feynman path integral. The
> space of all paths is (uncountably) infinite dimensional,
> and various tricks are used to perform the integral and
> extract simple numerical predictions.

Ok, but the word "dimensional" above is IMO a misnomer,
and it confuses me, if the word "path" is too simple then
couldn't we use "geodesic"?

> We can't get away from those pesky inf-dim spaces in QFT.

>
> >>> So we need to prove differential calculus and QT can merge,
> >> It's not so much differential calculus and QT", but rather
> >> "finding appropriate topologies and algebras that solve
> >> current theoretical physics issues rigorously."
>

> As I mentioned in another thread. The (mathematical) merging
> of differential calculus and quantum theory already goes
> under the name of "Lie Integration". That's actually an
> answer to my dearest Lord Ah Ha's question about "What would

> a unification of differential calculus and quantum theory

> entail?". Although Lie Integration is quite old in math
> circles, we are still rather a long way from carrying the
> programme through to completion in physics (imho).

>
> > Perhaps you would enjoy a High School level problem,
> > in QFT.
>

> "High School QFT"?? I'm pretty sure that's a contradiction
> in terms. (Or is it an "oxymoron"? Maybe both. ;-)
>
> > Let "a" and "b" be two separate charges. ....
> > ...

> > and we quantize the E-field by,
> >

>>a*b = F*r^2, Eq.(ab)

> Huh?? That's not quantization. (Quantization means taking
> the observables of a classical theory and constructing a
> unitary representation of them on a Hilbert space, such that
> the classical Poisson bracket maps over into commutators --
> or maybe the subtler Dirac-Bergman brackets in the case of a
> constrained theory, or gauge theory such as EM.)
>
> > ... If you are now provided with the EM field tensor

> > F_uv how would you explain the above?
>

> I don't understand what "problem" you want me to solve.
> Since there are 2 charged particles and an EM field, we have
> a multiparticle problem, so simple relativistic approaches
> can only be approximate. There is still no satisfactory
> interacting multi-particle relativistic quantum theory and
> we must resort to full QED if we want to do better. But QED
> is mostly about scattering, and doesn't handle bound states
> very well unless you drop back to a non-relativistic
> approximation.

Ok, (Sorry to frustrate you), lets begin where we left,

a*b = F*r^2 , Eq.(ab)

I'll do a mathematical experiment by suggesting
a GC (Generally Covariant) expression may be,

2ab = a*F_uv X^u X^v

but then that fails cuz a*b=0 cuz F_uv X^u X^v=0,
due to the asymmetry of F_uv in the summation.

So now I will be successful using,

2ab = a*F_uv(b) [X^u(a) X^v(b)] , Eq.(2ab).

With the field source arbituarily set to (b) in F_uv(b),
cuz it makes no diff to write b*F_uv(a) above.

For completeness, let's view the detail.
The spatial relations are,

X^i(a) = - X^i(b)

to signify "a" is in the opposite direction of "b",
as "b" to "a", however in time,

X^0(a) = X^0(b).

This expands to produce, (using just i=1),

a*F_01 X^1(a) X^0(b) = a*F_10 X^0(a) X^1(b).

Set F_10(b) = E(x) = b/r^2 and F_01(b)= - E(x).

X^1(a) X^0(b) = - X^0(a) X^1(b) = r^2

to obtain the result of Eq.(2ab).

By juggling units, let 2ab = 2h where "h" is
Plancks, (action = charge squared).

We needed Eq.(2ab) to merge classical
electrodynamics, via GC to Quantum Theory.
There's more....

> So... I guess still don't understand the issue that's
> bugging you.

I guess I'm ok now.

> Oh, and btw...
>
> > ...derivative of a photon...
>
> I still have no idea what you mean by this phrase. My
> dearest Sir Peter already expressed it succinctly when he
> said "... one cannot differentiate a classical body either".

>
> > We crafted our SPF charter without regard to consideration
> > of sexy stuff, IOW's we have no policy on that stuff.
>

> I wonder whether any children under 16 read this newsgroup.
> Doubtful, no? Anyway, I'm still a lot tamer than all those
> sexy videos that saturate free-to-air TV on Saturday
> mornings.
>
> Maybe I should try to get my own TV show.

XXX Jeopardy, can I be a contestant?

> ----
> LOL from the seriously straight-laced Princess!

Cheers
Ken S. Tucker

[Ken S. Tucker]

Hi Ah Ha and all.

On Aug 1, 12:50 pm, Ah Ha <ProfHarri...@gmail.com> wrote:

> On Aug 1, 9:01 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:

> > > > dX=0 , X=/=0 , X is not equal to zero.
>
> > > Ah, this is something I have thought about. Are you familiar with
> > > Hassler Whitney's paper, "A function not constant on a connected set
> > > of critical points"?
>
> > I am now!
>

> The example of Whitney shook up mathematics and showed the way to
> Morse when he proved Sards theorem. (Whitney's example is a
> counterexample to Sard if certain conditions are not met. In fact,
> Whitney was hard at work on Sard, but Morse beat him to it. They were
> at the IAS at the same time.) It is one of the best examples to know
> about in analysis as it shows how calculus can break down.

If convenient, provide a favorite link of yours on a subject
you bring up, for example my research begins here,
http://en.wikipedia.org/wiki/Morse_theory
if that's what you'd recommend?

> > > He came up with a function f:R^2 -->R which is
> > > continuously differentiable and has a connected path of critical
> > > points, but f is increasing along the path. The path has to be
> > > nonsmooth, of course, otherwise the fundamental theorem of calculus
> > > would be contradicted. However, if your function is smoother than the
> > > path is rough (you can use Hausdorff dimension to make this precise),
> > > then the function must be constant along the path.
>
> > That reminds me of a wheel rolling on a rough surface.
> > As the wheel shrinks, singularities can be encountered,
> > but expanding the wheel large enough and they vanish.
> > I can work that analogy of continuum and quantum, if
> > it's ok with you.
>

> Good analogy with regard to integration of smooth forms over rough
> surfaces. Say more, if you like:-)

Ok, for general interest. I studied the evolution of car
wheel diameter and as the roads improved the wheel
diameter shrank. I see you're a cyclist, (is that right?)
http://math.berkeley.edu/~harrison/
I found that a bicycle with big wheels is smoother on
rough terrain than one with wee wheels.

Another issue is measuring shoreline length.
(It even has legal issues).
How long should our measuring rod be !?!. (rhetorical).
As the measuring rod reduces, the shoreline length
increases. I'll push to a limit of the rod=>0 then
every atom on the shore becomes an island at the
nanoscopic level, and the shoreline length=>oo.
Do you sniff Zeno's paradox !?!

> > Planck gave birth to Quantum Theory by taking the limit
> > h => constant INSTEAD of h=>0.
>

> What limit?

I'll ref to "Introduction to Modern Physics" by
Richtmyer, Kennard and Cooper, pg. 129, and
then adlib the classical approach to obtain the
average energy of an oscillator requires h=>0,
it was Planck's Quantum Hypothesis that used
h=> finite number, to invent Planck's constant.

> > Suppose we compare that to a differential coefficient,
> > dx/dt=0 to an incremental DX/DT =/=0, where we'll
> > *assume* x=X and t=T to start. The question is,
> > is the process of taking the "limit" an issue or is the
> > assumption x=X, t=T faulty?
>

> I do not understand =/= notation,

That's ascii for "not equal to", some use "<>".

> nor the lower case and upper case
> use of x and t.

This returns us to the "derivative of a photon".
Pardon my childish analogy, I can give you
one penny per minute, but I cannot give you
a 1/2 penny every 30 seconds, nor a 1/4
penny every 15 seconds etc, hence the
"topology" forbids dx/dt but permits DX/DT.

In introductory differential calculus we use the
Limit, of the increment,

LIM DX/DT => dx/dt as dt=>0,

but that *implicity* assumes the topology of X
(where X can only have quantized values like
1,2,3,4 ...pennys) is equal to x (where x may
have fractional numbers).
X=/=x for pennies.

Of course for continous curves X=x.

Those details apply to time too. It's impossible
to measure dt, as our best Cs clocks measure
DT, (see atomic clock standards for details).

Furthermore length is now defined by time,
see Modern SpaceTime at this link,
http://physics.trak4.com/
for a few brief notes.

> But I live in the aether!
> A.H.

Regards
Ken S. Tucker
PS:Do you have something online about "quantum
calculus"?

[Ken S. Tucker]

Hi Princess et al...
Studied your post carefully.

On Aug 1, 8:51 pm, neurop...@yahoo.com.au wrote:
> Ken S. Tucker wrote:
> > My lab pals called me Katy, (from KT).
>

> "Katy" it is, then.

I think I got that name cuz I get flustered around
women of the opposite sex.

> >> ... infinite dimensional space ...

> > What bothers me is the semantics of "degrees of freedom"
> > being equated to "dimension". The distinction is vital when
> > Dimensional Analysis is being done.
>

> "Dimension" is nothing more than the number of linearly
> independent elements in the abstract vector space being
> considered. Is there perhaps a mixup here between the
> mathematical notion of "dimensions" and the physical notion
> of "units"? Or between "dimension" and "type".

Ok, usually the Kronecker Delta (& is a partial)

&x/&y =0 , &x/&x=1

defines the dimensional independence, and of
course that's fundamental to tensor analysis.
In GR physics that is confined to 4D, 3 space
and 1 time. One may generalize to infinite D,
but is that physics or semantics !?!.

> Consider a square-integrable complex-valued function f(x)
> where x \in R^3. That is, \int d^3x f*(x) f(x) is finite,
> (where the integral is over all R^3).

ok, as an axiom.

> Now consider the set of *all* such square-integrable
> functions, sometimes denoted as L^2(R^3). For any two
> functions f,g in this set, h := (f+g) is also a function in
> the set (since h is square-integrable too). Similarly, cf is
> also in the set (where c is any complex constant). In fact,
> the set L^2(R^3) satisfies all the axioms of a vector space.
> Seehttp://en.wikipedia.org/wiki/Vector_space

ok.

> Now, what's the dimension of L^2(R^3)? (Ie, what's the size
> of the largest subset of linearly independent elements of
> that set?) Infinite, right? So we have an infinite
> dimensional vector space (called a "function space").

ok.

> The *types* of the domain and range of such functions are
> probably what's more important when doing "Dimensional
> Analysis" in physics. The word "Dimensional" here is a
> misnomer, and maybe "Type Analysis" is a better name for
> this.

Interesting, the traditional sematic is "Dimensional
Analysis" composed of Length, Time and Mass.
Physics is a bridge from Math to Engineering and
of course experimental physics.

> (Of course, there's no hope of changing this now, and
> one must become bilingual.) One can have two sets of
> elements of different types, but the sets can be isomorphic,
> with the same dimension. (I can have a set of 47 oranges, and
> another set of 47 sheep. The sets are isomorphic and have the
> same dimension, but they're of different types.)

I think I understand, the 47 is invariant, but you
intend to create an infinite number of types, like
oranges, sheep, pink fairies of varying shades etc.
ok, I'm with you, and I understand the "bi" thing to,
but I'm keeping an eye on practical applications.

> >> ... to obtain such simple numbers which can usefully be

> >> compared with experiment typically requires some form of
> >> integration over the underlying infinite dimensional space.
> >> A common example in QFT is the Feynman path integral. The
> >> space of all paths is (uncountably) infinite dimensional,
> >> and various tricks are used to perform the integral and
> >> extract simple numerical predictions.
>
> > Ok, but the word "dimensional" above is IMO a misnomer,
> > and it confuses me,
>

> "Dimensional" is the correct word from a strict mathematical
> viewpoint. Maintaining a clear distinction between
> "dimension" and "type" is important to think in a clear
> headed way about this stuff.

ok.

> > if the word "path" is too simple then couldn't we use
> > "geodesic"?
>

> Not when we're talking about Feynman path integrals. The
> nearest thing there to "geodesic" is the classical path that
> minimizes an Action. But the paths of Feynman which all
> begin and end on a given pair of Cauchy surfaces can jump
> around all over the place in between. Definitely not
> geodesics in general. Each path can be expressed as a
> function p(x,t) and the inf-dim space of all such functions
> is the space we're trying to integrate over when performing
> a path integral.

Right. I was thinking of each geodesic as having a
probability ingrained along the path, such as dropping
a ball into a peg board then arriving at a distribution.

> >> ....

> > Ok, (Sorry to frustrate you), lets begin where we left,
>
> > a*b = F*r^2 , Eq.(ab)
>

> Actually, I didn't understand what you were doing before to
> reach even this point. It seemed like you were considering
> the classical fields of two point charges, but your notation
> is too ambiguous for me to make clear sense out of it.
> The moderator previously said...
>
> > I let this through, because most readers are used to Ken's
> > neglection of the vector character of E, and the use of the
> > same symbol, F, for 2 different entities ;-)

Fella's I may have over simplified, here's a link on F,
http://en.wikipedia.org/wiki/Coulomb's_law#Scalar_form

> Unfortunately, this delicate reader is not so used to it, so
> you'll have to tighten up your notation for me to understand
> it correctly. Maybe you should start a fresh thread stating
> the problem again with all the correct types, indices, etc?

ok. There's always a trade-off between being flippant
or too detailed, and ascii math sux a bit, so we need
to be a bit patient, I'll try to do better.

> (Methinks Sir Jay is probably now quite dismayed at how far
> his original thread has been shamefully hijacked.
> Forsooth! Where are our manners?)

Hey Jay enjoyed "derivative of a photon", sometimes
thread drift is good stuff, it's all related, hard to draw
lines.

> ----
> LOL from Princess Somewhat-Perplexed!

I have some spare *de-Perplexing* I can send you,
let me check the expirey date..., oops, no wonder
I'm a bit slow.
Regards
Ken S. Tucker (Katy)

[Ken S. Tucker]

Hi Princess and all.

On Aug 2, 6:44 pm, neurop...@yahoo.com.au wrote:
> Hi Katy,
>
> > Studied your post carefully.
>
> Always wise to listen carefully before speaking.
> I'm continually amazed how many people don't do that.

Your posts are often very deep, I enjoy re-reading
quite a few times, I'm sure others do too.

> >> "Katy" it is, then.
> > I think I got that name cuz I get flustered
> > around women of the opposite sex.
>

> Sounds like Radar O'Reilly?
> Try teasing them mercilessly - it works for me. :-)

LOL, I tried that, do you know what XXX "crashed
and burned" means?

> >> "Dimension" is nothing more than the number of linearly
> >> independent elements in the abstract vector space being
> >> considered. Is there perhaps a mixup here between the
> >> mathematical notion of "dimensions" and the physical notion
> >> of "units"? Or between "dimension" and "type".
> > Ok, usually the Kronecker Delta (& is a partial)
>
> > &x/&y =0 , &x/&x=1
>

> > defines the dimensional independence, ...
>
> No, that's "functional independence". It's saying that
> x is not a function of y.

ok.

> > In GR physics that is confined to 4D, 3 space and 1 time.
> > One may generalize to infinite D, but is that physics or
> > semantics !?!.
>

> I think you might have missed the point of my previous
> explanation of inf-dim function spaces. There can (in
> general) be an infinite number of different functions over a
> given 4D base manifold. The field equations then restrict
> this inf-dim function space down to a smaller one, and if we
> impose initial/boundary conditions we (hopefully) get a
> unique function. But to compute scattering amplitudes in
> quantum gravity (eg in Hawking's stuff about black hole
> information loss, or non-loss) we need to pay more careful
> attention to the inf-dim function space.

In tensor analysis the usual assumption is to consider
the indices as integers, such as in 4D, u = 0,1,2,3 in GR's
ds^2 = g_uv dx^u dx^v.
I've studied non-integer (continuous) indices, a simple
demonstration of the continous variation of dimensionality
is found at this link,
http://en.wikipedia.org/wiki/Fractional_calculus
though I'm digressing somewhat from your meaning.

> >> The *types* of the domain and range of such functions are
> >> probably what's more important when doing "Dimensional
> >> Analysis" in physics. The word "Dimensional" here is a
> >> misnomer, and maybe "Type Analysis" is a better name for
> >> this.
> > Interesting, the traditional sematic is "Dimensional
> > Analysis" composed of Length, Time and Mass.
>

> If you stand back and think about it as "Type Analysis"
> instead, you'll get a deeper insight. Eg: length, time,
> mass, charge, angle, momentum, angular momentum, isospin,
> color, are all "types". "Length/time" is a different type
> from plain "length", and also a different type from
> "Length/time^2". We then make more unified sense of all
> these disparate types by pulling them together such that
> they arise out of an algebraic or group-theoretic framework.
> Eg: several things can then be said to be of the same "type"
> if they obey the algebra that defines that type.

Yes. What I have learned is express things Generally
Covariantly (GC), in tensors, then "group" them by
their characteristics, rank, covariant, contravariant,
symmetry and asymmetry. Are you ok with tensors?

> > Physics is a bridge from Math to Engineering and of course
> > experimental physics.
>

> Yes, there's "pure" mathematicians, "applied"
> mathematicians, mathematical physicists, theoretical
> physicists, phenomenological physicists, experimentalists,
> theoretical engineers, handle-cranking engineers, managers,
> sales people, ... the distinctions are endless. It's a pity
> that University courses don't include a semester on
> "Diplomacy for Really Smart Buggers". Then there might be
> fewer counterproductive arguments.

I have a secret philosophy: If a mathematics can be physically
demonstrated, it is real a math, otherwise it's imaginary.

> >> One can have two sets of elements of different types, but
> >> the sets can be isomorphic, with the same dimension. (I can
> >> have a set of 47 oranges, and another set of 47 sheep. The
> >> sets are isomorphic and have the same dimension, but they're
> >> of different types.)

> > I think I understand, the 47 is invariant, but you intend to
> > create an infinite number of types, like oranges, sheep,
> > pink fairies of varying shades etc.
>

> No, the "47" thing was only to illustrate the distinction
> between "dimension" and "type". Both those sets have
> dimension=47, but they're of different "type". In physics we
> typically deal with a finite number of types but we concoct
> inf-dim spaces based on these types.

You're stretching my neurons to pulp.

> Imagine now that we have another set of sheep, but this time
> there's an infinite number of sheep in the set. Similarly,
> imagine a set with an infinite number of oranges. What does
> it mean to ask whether these sets have the same dimension?

It's difficult to imagine something that is physically
impossible, but I can imagine a continuous increasing
amount without end.

> We must establish whether or not an isomorphism exists
> between the sets (ie, a 1-to-1 correspondence: every sheep
> corresponds to one and only one orange, and vice versa).

What if each sheep eats one orange :-)?
That establishes a 1-1 relation.

> > but I'm keeping an eye on practical applications.
>

> Quantum Field Theory has very practical applications. :-)
> LOL from the Princess!

Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Ah Ha et al.

On Aug 3, 8:28 am, Ah Ha <ProfHarri...@gmail.com> wrote:
...

> > Another issue is measuring shoreline length.
> > (It even has legal issues).
> > How long should our measuring rod be !?!. (rhetorical).
> > As the measuring rod reduces, the shoreline length
> > increases. I'll push to a limit of the rod=>0 then
> > every atom on the shore becomes an island at the
> > nanoscopic level, and the shoreline length=>oo.
> > Do you sniff Zeno's paradox !?!
>
> > > > Planck gave birth to Quantum Theory by taking the limit
> > > > h => constant INSTEAD of h=>0.
>

> Your previous paragraph now explains Planck's idea. Thanks.
> You are right, that everything comes down to how one takes
> a limit, i.e., to topology and algebra.

Thanks Ah Ha for the confirmation. As a student and
then a tutor on differential calculus that Limit has been
a difficult step, but you've clarified things. Maybe there
is more logic to that Limit than we presumed.

> > PS:Do you have something online about "quantum
> > calculus"?
>

> Not yet.
> I have taught the new calculus to Berkeley students in three courses,
> but the notes have not been made public. (My website has not been
> updated in several years.) Each time I teach it, the theory becomes
> simpler and stronger and we start again, reproving everything from
> scratch the next time.

Understood, it's in ongoing evolution, hard to stop
and benchmark, that brakes the creative momentum.

> At this point it has evolved to become a
> discrete theory with convergence to the smooth continuum, and has some
> quantum aspects. I am now hard at work on a monograph, and have just
> been given some research time to work on the theory (including physics
> applications). I had not intended to say anything, but your
> intriguing comment about photons hit close to home.

I'd be happy to help out, if I can, via open forum or via
email if you want, but I understand you're on a learning
curve...yahoo.

I read of your interest in "Dimension Theory", perhaps
a GR sample might interest you.
As you know the orbit of Mercury's perihelion rotates
43" per century.
As it turns out, that same effect can be approximated
by modifying Newtons gravitation at Mercury's range
from the Sun by modifying the exponent "2", to,

Acceleration = GM/r^(2.000 000 18).

Area is proportion to r^2 , Volume to r^3, but there is
something between them in nonorthogonal spacetime,
isn't that nifty!?! That's how I got into Fractional Inter-
dimensional Transformations and Fractional Calculus.
Regards
Ken S. Tucker

PS: My current hobby is converting nonorthogonal
(warped, wowwed and twisted) pieces of lumber to
integrate to become an orthogonal box,
http://www.flickr.com/photos/dynamics/

[Ken S. Tucker]

Hi Ah Ha & MODERATOR"S.

On Aug 3, 2:58 pm, Ah Ha <ProfHarri...@gmail.com> wrote:
> > ======================================= MODERATOR'S COMMENT:
> > I apologize for the passing of the statement that the essence is in the limit procedure, for the central notion of physics is that of state
>
> You did not err in letting this pass. From the classical viewpoint,
> you are correct. I apologize that I must ask you to wait a bit to
> see what I meant. Sometimes it takes an outsider to see something
> new -- all of which reminds me to get back to work.

The SPF Charter is designed to encourage this
type of informal discussion, and one sometimes
uses an informal expression like: The Nature of the
Limit depends upon topology: get's us on the same
page, without a rigorous paper, and then "the domain
of appliance" of differential calculus, happens to be
a shared concern of Ah Ha and myself, per her ref
to the "breakdown of calculus", a few posts ago.
I think it's is an excellent discussion, sharpens me.
Everybodies happy!!!
Regards
Ken S. Tucker

[Ken S. Tucker]

Good AM Princess and all.
I should mention to start that Jay, Fred and I have
Zee's "Quantum Field Theory in a Nut Shell" and
Fred and I have Weinberg's "Quantum Theory of Fields,
Vol. 3", as common refs.

On Aug 3, 11:03 pm, neurop...@yahoo.com.au wrote:
> Hi Katy,

> > Your posts are often very deep,
>
> Hey, if I try really hard I can brain-fart the entire
> breathable atmosphere out of a lecture theatre.
> (I think I'm about to do it again in this post, so
> sensitive noses be warned!)

Smells like prefume :-).

> >> Try teasing them mercilessly - it works for me. :-)
> > LOL, I tried that, do you know what XXX "crashed and burned"
> > means?

> It means you forgot to laugh as your biplane was being
> shot at.

I got spanked.

> > I've studied non-integer (continuous)
> > indices, a simple demonstration of the continous variation
> > of dimensionality is found at this link,

> >http://en.wikipedia.org/wiki/Fractional_calculusthough I'm

> > digressing somewhat from your meaning.
>

> Yes, it's digressing, but I can bring it back on track by
> noting that the differential operator d/dx can be regarded
> is a linear operator on a space of functions. Thus, d/ds
> acting on a function f(s) is an inf-dim generalization of a
> matrix A acting on a 3-vector v. Both are mappings from one
> vector to another, but in the former case the vectors are
> infinite-dimensional, with continuous index "s".
> Sometimes I find it is useful to write f(s) as f_s to
> emphasize this.
>
> Viewed in this way, operations like "taking the square root
> of a derivative" can be treated in analogous ways to "taking
> the square root of a matrix". In Functional Analysis there
> are various theorems (eg polar decomposition) that tell you
> when such operators can be decomposed into products of other
> operators. (Functional Analysis is basically Linear Algebra
> for infinite-dimensional vector spaces.)

>
> > What I have learned is express things Generally Covariantly
> > (GC), in tensors, then "group" them by their
> > characteristics, rank, covariant, contravariant, symmetry
> > and asymmetry. Are you ok with tensors?
>

> Yes, thoroughly. But you're only talking about tensors in
> the context of the diffeomorphism group which I find a bit
> boring. It was a revelation when I eventually came to see
> such things in the context of irreducible representations of
> arbitrary Lie groups. That's far more important to quantum
> theory, particle physics, and even quantum gravity.

Yes, but I think tensors are foundational, and one must
be able to *return* to them, that's the hard part.

> For the diffeomorphism group, you can pretty much classify
> its irreducible representations in terms of tensor rank and
> their symmetry/anti-symmetry properties. Eg, you can't turn
> a symmetric tensor A_uv into an antisymmetric one by any GR
> transformation. Thus, the symmetric and antisymmetric rank-2
> tensors can be seen as distinct irreducible representations
> of the group. (That's not quite the correct math way of
> expressing it, but I'm just trying to convey the intuition.)

Yes, though a tool for an arbituary tensor is the sum,

A_uv = 1/2(A_uv + A_vu) + 1/2(A_uv - A_vu) and

that applied to the metric gives,

g_uv = s_uv + a_uv .

> Similarly, elementary particle types can be classified
> according to the (unitary) irreducible representations of
> the Poincare groups. Then there's also the irreducible
> representations of the internal symmetry groups,
> SU(2)xU(1)-electroweak, SU(3)-color, etc, etc. Lie group
> theory is at the core of it all - I now find it much deeper
> and interesting than boring old GR with its diffeomorphisms.
> (Of course, if one wants unified theories, one must start
> trying to work with unitary irreps of the diffeomorphism
> group, but I *definitely* won't get into that here.)

Well that's certainly one approach.

> Suffice to say that any aspiring theoretical physicist needs
> to understand very deeply the principle that "elementary
> particle types" *are* "unitary irreducible representations
> of certain Lie groups". Various composite-particle problems
> are then analysed by taking tensor products in those groups
> and examining the representation theory thereof. The
> standard case is the stuff about the Clebsh-Gordan
> coefficients which one encounters in the theory about a
> system composed of two particles of different spins can be
> decomposed into a sum of various other spin values.
> (Eg, a product of two spin-1/2 particles can be expressed
> as a *sum* of spin-0 and spin-1.)

1/2 - 1/2 =0 , 1/2 + 1/2 =1

> So "tensors" have a much wider applicability than just the
> GR context.

Certainly.

> (Actually, any Feynman diagram is just a diagrammtic
> representation for complicated contractions of certain
> tensor products of inf-dim spaces.)

>
> > I have a secret philosophy: If a mathematics can be
> > physically demonstrated, it is real a math, otherwise it's
> > imaginary.
>

> Psst! Wanna hear an even deeper secret? The physical space
> you think you live in is really an abstract mathematical
> space. (Oh, watch the fur fly now!)

We're ok.

> >> ... the "47" thing was only to illustrate the distinction

> >> between "dimension" and "type". Both those sets have
> >> dimension=47, but they're of different "type". In physics we
> >> typically deal with a finite number of types but we concoct
> >> inf-dim spaces based on these types.
> > You're stretching my neurons to pulp.
>

> Oh? My pseudonym "neuropulp" was meant to refer to me, not what
> I do to others.
>
> Are you then not yet familiar with the inf-dim Fock space
> of QFT?

I'm a student of the subject. I try to stay finite unless
a cosmology problem is discussed.

> >> Imagine now that we have another set of sheep, but this time
> >> there's an infinite number of sheep in the set. Similarly,
> >> imagine a set with an infinite number of oranges. What does
> >> it mean to ask whether these sets have the same dimension?
>

> I should mention again that these are in fact bad examples.
> I should have tried harder to think of an example involving
> bona fide vector spaces rather than just structureless sets.

> > It's difficult to imagine something that is physically
> > impossible, but I can imagine a continuous increasing amount
> > without end.
>

> Careful. There are hints and puzzles in QFT that such
> "unimaginable" inf-dim spaces are actually important
> physically. In finite-dimensional QM, there's a theorem
> (Stone-von Neumann) which says that all unitary
> representations of the canonical commutation relations are
> equivalent. That means we can pick whatever Hilbert space we
> want if its degrees of freedom correspond to those of the
> physical system. The physical equivalence of the difference
> choices ensures we can pick the one that's the most
> mathematically tractable.
>
> But the proof of the Stone-von Neumann theorem fails for the
> inf-dim case. Two inf-dim representations of the CCRs can be
> "unitarily inequivalent". This is actually important in
> condensed matter physics (superconductivity, etc). The
> Hilbert space applicable at room temperature is inequivalent
> to the Hilbert space that we need to use at very low
> temperatures. (Look up "Bogoliubov transformation" if you
> want to know more.)
>
> Something bizarre is going on with inf-dim quantum theory,
> and we still don't really understand it (imho). But they do
> indeed seem relevant to physics -- which can be a bit of a
> shock when you first encounter it.

>
> >> We must establish whether or not an isomorphism exists
> >> between the sets (ie, a 1-to-1 correspondence: every sheep
> >> corresponds to one and only one orange, and vice versa).
> > What if each sheep eats one orange :-)? That establishes a
> > 1-1 relation.
>

> Exactly - you've established that both sets are isomorphic
> to the (positive) integers.
>
> But now, given the same set of an infinite number of sheep,
> can you establish an isomorphism between those sheep and
> the set of points between 0 and 1 on the real line?

Yes, because everything is relative. Allow me to be romantic,
you Princess and I Katy are relating. The absolute values
are Princess=Princess and Katy=Katy but if that was all there
is, niether of us would "correspond", nor relatively exist, but our
communications provides a relative (relational) existance that
is 1 to 1, somewhat along the lines of Newton's 3rd Law, that
is an inter-action.

> (And
> don't start talking about quantizing the line. I'm saying
> "real line" here in its strict mathematical meaning.)

Ok :-).

> LOL from the Princess!

Regards
Ken S. Tucker ...(Katy)

[Ken S. Tucker]

Hi Princess et al.

On Aug 4, 11:05 pm, neurop...@yahoo.com.au wrote:
> Hi Katy,
>

> > I should mention to start that Jay, Fred and I have Zee's
> > "Quantum Field Theory in a Nut Shell" and Fred and I have
> > Weinberg's "Quantum Theory of Fields, Vol. 3", as common
> > refs.
>

> Vol 3? Supersymmetry? What about Vols 1 & 2?

I chuckle at the *buzzword* "super" in front of so many
things...what's next ultra. Anyway, good to hear you
have those common refs, (I'm sure Princess Ah Ha
has them too), although physical confirmation is
pending.

> In any case, Zee and Weinberg are at opposite ends of the
> bookshelf. Zee is very introductory, and Weinberg is very
> advanced.

I use Weinberg's "Grav&Cosmo" as one standard text,
and see his style as "detailed" as he tries to stay close
to physics and tensors, same in QFT3. Do you have
that available? (Fred does too).

> You need something in between. Maybe Peskin &
> Schroeder, and Weinberg Vol 1?

I rely on quite a bit on Ziman's "Advanced Quantum Theory",
(scribbled with notes).

> >>> Are you ok with tensors?
> >> Yes, thoroughly. But you're only talking about tensors in
> >> the context of the diffeomorphism group which I find a bit
> >> boring. It was a revelation when I eventually came to see
> >> such things in the context of irreducible representations of
> >> arbitrary Lie groups. That's far more important to quantum
> >> theory, particle physics, and even quantum gravity.
> > Yes, but I think tensors are foundational, and one must be
> > able to *return* to them, that's the hard part.
>

> Lie algebras are foundational. Tensors are built on top of
> them (actually, on top of their representations).

Well algebra uses x^2 + x, but one cannot add Area
and Length, hence "x" is a scalar, but I'm coming
from the rather humble position of applied physics.

> >> Thus, the symmetric and antisymmetric rank-2
> >> tensors can be seen as distinct irreducible representations
> >> of the group. (That's not quite the correct math way of
> >> expressing it, but I'm just trying to convey the intuition.)
> > Yes, though a tool for an arbituary tensor is the sum,
>

> > A_uv = 1/2(A_uv + A_vu) + 1/2(A_uv - A_vu) and ...
>
> Hey, congratulations! You've just performed a simple
> decomposition into irreducibles.

Thank you;-). IIRC one can generate an infinite series.

> >> (Eg, a product of two spin-1/2 particles can be expressed as
> >> a *sum* of spin-0 and spin-1.)
> > 1/2 - 1/2 =0 , 1/2 + 1/2 =1
>

> That much is just vector addition of angular momenta. It
> gets more complicated if you want to see how a tensor
> product of two spin-1/2 fields decomposes into a sum of
> spin-0 and spin-1 fields (including the correct
> multiplicative constants).

Yes, I've pondered that, in photon emission,
I ended up with a graviton.

> >> But now, given the same set of an infinite number of sheep,
> >> can you establish an isomorphism between those sheep and the
> >> set of points between 0 and 1 on the real line?
> > Yes, because everything is relative.
>

> Oops! You just failed Real Analysis 101. It can be proven
> rigorously that no such isomorphism exists.

Depends upon your philosophy of relativity, but really
I agree with you, Network Analysis and Economics
for example are non-physical, imaginary concepts
but very real in our world, when the bills come in.

> > Allow me to be romantic, you Princess and I Katy are
> > relating. The absolute values are Princess=Princess and
> > Katy=Katy but if that was all there is, niether of us would
> > "correspond", nor relatively exist, but our communications
> > provides a relative (relational) existance that is 1 to 1,
> > somewhat along the lines of Newton's 3rd Law, that is an
> > inter-action.
>

> Whoa! Never enter any rally driving competitions! You just
> failed to take a bend and drove straight off into thin air.
> (Translation: all that has nothing to do with the question.)

Major Tom (Katy) thrusted to escape velocity when she was
supposed to retro for orbit...lost in space...again!

> Nevertheless, you might enjoy the Merman's "Ithaca"
> interpretation of Quantum Mechanics. The basic idea (iirc)
> is something like "only correlations has physical reality,
> that which they correlate does not". If you search on
> Google Scholar it should be easy enough to find the paper.
> Rovelli's relational stuff also has ideas along these lines.

1+1=2 is complicated because it involves a relation
between each one. Consider a love relationship, is
it you or me or what bridges us? I think the bridge.

> ----
> LOL from Princess Tow-Truck-Driver.

Thanks, you'll need a SpaceShip.
Regards
Ken S. Tucker ....(Katy)

[Ken S. Tucker]

To Ah Ha and all.
While Ah ha is gone, I try to sturdy things up a bit while we
await her glorious return.

On Aug 4, 1:16 pm, Ah Ha <ProfHarri...@gmail.com> wrote:
...
> One does see them all over the place in quantum theory. As you point
> out in another post, the Stone Von Neumann theorem does not hold in
> infinite dimensions. Once my paper is out, it will be easier to
> discuss the remarks and questions I have about Hilbert space core
> possibilities. Once more, I do apologize. I had intended to remain
> silent until the paper was ready, but the brave knight KT had to talk
> about the impossibility of differentiating photons, and you keep
> linking mathematics and physics with remarkable verve. Now if you
> two will just stop saying interesting things and making me laugh, I
> can exit. Until later... (If you do not hear from me for awhile, it
> is no reflection on you.)
> AhHa

I'd like to discuss the "differential of a photon" in a
more rigorous context, using GR's vanishing covariant
derivative of the metric g_uv;w=0, with the "Hi&Lois"
("w" is an arbituary parameter index), gedanken provided
in this article,
http://physics.trak4.com/MST_UFT.pdf

Once the metric g_00 of GR is equated to Power W_00
by way of Conservation of Energy (CoE), we are obliged
to find W_00;w=0 vanishes, however the Power is not
constant.

So we can solve that particular derivative by using,

(W_00 + DW_00);w=0

W'_00 = W_00 + DW_00

where DW_00 is an increment of Power, such as a
photon, and is NOT continous since DW_00;w =0,
and still allows Power to change incrementally.

The foundation of g_uv_w=0 is (IMO), the Principle
of Equivalence (PoE) , wherein in a freefall frame,
the local metric g_uv become constant relatively
to that inertial frame, rendering the vanishing of
g_uv;w and subsequently W_00;w via CoE.

That gives a sound theoretical foundation to "Planck's
Quantum Hypothesis" rested upon GR's PoE.

The logic of the Quantum Theory and subsequent
developements can be founded on GR, assuming
I haven't screwed up :-).

Regards
Ken S. Tucker
kxsxt8

[Ken S. Tucker]

Hi Jay

On Aug 5, 10:05 am, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:
> Hello to all:
>
> Two threads down, titled "Why stop at the acceleration operator for
> calculating Zitterbewegung? -- Reply to Ah Ha -- And Maybe a Connection
> between Gravitation and Quantum Theory?," I gave our playmate Princess
> Neuropulp some spanking material. Here, I will offer even more, in
> order to see who really has the largest cheeks around here. ;-)
>
> This new material is at:
>
> http://jayryablon.files.wordpress.com/2008/08/quantum-time-dependence...
>
> and is a three-page "blueprint" for a quantum / gravitational union.
> This link develops the closing thought in that thread, which I will
> repeat here to widen the target a bit, namely:
>
> In other words, as soon as quantum theory forces us into the "constant"
> alpha becoming a function of time, then the "constant" gamma become
> functions of time. And, the spacetime metric becomes a function of
> time. And, the metric therefore is no longer "flat" as was originally
> assumed. And now, we have gravitation!!!, courtesy of Werner
> Heisenberg's insistence that in quantum theory!!! we take time
> derivatives by canonically commuting with the Hamiltonian. (This can be
> further generalized as well to space derivatives, commuting with
> momentum operators which are analogs of the Hamiltonian, so now the
> spacetime is everywhere not flat but bubbling with zitterbewegung. And
> we are then into topology and all the other things in Neuropulp's "brain
> fart.") Suddenly, gravitation and quantum theory are united. Voila!
>
> Looking forward to some flying fur, ;-)
>
> Jay.

Weinberg wrote a chp #31 in QFT3, entitled "Supergravity"
and onward to the "supermetric", that's *looks* similiar to
your treatment, but I think yours is better.
If you have access to that book, also see "Veirbein Formalism
appendix" to connect his Eq.(31.1.9) to Eq.(31A.1) in the
appendix. I think it's worth a look.

I liked the 1st part of Weinberg's approach but toward the
end, it seemed not to close well by leaving loose ends, IMO,
but that's another topic.

On supergravity, I poked around on the net and didn't find
anything yet, that's as good as Weinberg's.
What he does in the refd Eq.(31.1.9) is to add a spin to a
veirbein.
Cheers
Ken S. Tucker

[Ken S. Tucker]

Hi Princess.

On Aug 5, 8:18 pm, neurop...@yahoo.com.au wrote:
> I said,

>
> >> Lie algebras are foundational. Tensors are built on top of
> >> them (actually, on top of their representations).
>

> Katy said,

>
> > Well algebra uses x^2 + x, but one cannot add Area and

> > Length, hence "x" is a scalar, ...
>
> I said "Lie" algebras (and their representations), not
> "polynomial algebras over the reals". "Area" and "length"
> are applicable to different representations of the Lie
> algebra se(3) so of course you can't sensibly add them.

Ahhh, but you can! As I explained, using Fractional
Interdimensional Transformations, (FITs), tensors
can handle that, I provided a physical demo to
Princess Ah Ha using Mercury's orbit.

> (I'm guessing you haven't studied Lie algebras/groups yet?)

I use it informally, it's a bit simple, for tough stuff I
do the more long handed tensor proofs.

> >http://physics.trak4.com/MST_UFT.pdf

> In the 2nd para of your article it says:
>
> > mass is defined by the covariant 4-vector Energy-Momentum
> > component, P0 ,
>
> That means your "mass" is not Lorentz invariant, hence does not
> correspond to the standard relativistic mass.

Thanks, your right, I should have specified *rest* mass,
please see,
http://physics.trak4.com/MST_Mass-Definition.pdf

> Later you write:
>
> > Power = W_00 = energy/time = P_0 /x_0 .
> > That Power W_00 transforms as g_00,
> > IOWs theyre identical except for constants.

Yes, those "constants" are derived from quite
sophisticated methods, but in a brief, they're
usually set to "1".

> Saying "transforms" is meaningless unless you specify the
> group. I presume you're talking about GL(4) or maybe the
> full group of diffeomorphisms on a Riemannian manifold.

Tensors use a *proper transformation*, that is well
defined.

> In
> any case, P_0/x_0 is not a tensor (you'd need at least
> P_u/x_v in SR, and more likely P_u;v in GR).

Of course, P_0/x^0 is a component, in the CS defined
by Modern SpaceTime.
http://physics.trak4.com/modern-spacetime.pdf

Once the CS is choosen, many of the usual tensor
analysis operations cannot be performed, that gets
tricky, and often see that error.

> Similarly, equations like your "g_00 = 1- W_00" are not
> tensor equations.

Yes that's correct, it's an application.

> The rest of the stuff about "potentials" a/r and b/r is
> ill-defined since you haven't specified where the positions
> of the "charges" (presumably you mean point charges).

Yes, that's right, "point" charges.

> Ok, that's all I have time for right now.

Thank you for your kind analysis.

> (I'll send the bill later.)

and I'll send you mind.

> Princess Spank-A-Lot, Inc.
> Customized Pleasure Services. "We'll touch you deeply."

This,
http://physics.trak4.com/MST_UFT.pdf
is an informal brief to colleagues relating Power
to GR's g_00 via the red-shift to show how MST
is compatible with known physics. In addition,
IMO, the most important thing to understand about
GR applied to gravitation is the red-shift, but usually
that's explained in terms of frequency and energy,
so I used the "Marshmellow gedanken" to see the
effect in terms of the Power "red-shifting".

Power however is quantized, so I couldn't really
use dPower so instead I had to use DPower.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Charles, Jay and all.

On Aug 7, 10:57 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
> >Hi Charles, Princess, Jay and all.
>
> >On Aug 7, 1:05 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >> Thus spake neurop...@yahoo.com.au
>
> >> >> did you read "supermetrics", as I suggested? If so what's
> >> >> your opinion?
>
> >> >You mean ch31 in Weinberg Vol-3? From a physics perspective,
> >> >all of the supersymmetry stuff in vol-3 is pure speculation.
> >> >That battleship may be of beautiful design, but we do not
> >> >yet know whether it's made of steel or sugar, and whether it
> >> >will float or dissolve when tested by launching down a
> >> >slipway.
>
> >Yes, I think Weinberg could have connected us a bit
> >better to physical reality.
>
> Surely to do that he would have had to omit the chapter.
>
> >> How will we ever know? The battleship is landlocked. The builders took
> >> no account of the requirements of a slipway.
>
> >Jays thrust to derive gravitation from QT looks very
> >reasonable.
>
> I didn't think so.

Ok, I do think Jay's article was weak on physical connectedness,
and went too fast to detailed math, but that's my subjective.

> >Way back to deBroglie expressing mass
> >in terms of waves, and extending from that to Dirac,
> >we should expect those waves should have a solution
> >giving the "Schwarzschild Solution", synonymous with
> >the meaning of Guv=Tuv.
> >Those waves should also be subject to "red-shift"
> >while at the same time creating the g-field, but to do
> >that, we'll need to use a curved spacetime, and so
> >I think we need to go generally covariant where wave
> >equations are concerned.
>
> Is this not just a failed approach to quantum gravity that people have
> been trying for half a century.

Consider the energy density Tuv compared to probability
density in Wave Mechanics. The integration appears (to
me) to render the same particle.
de Broglies "extended" wave becomes analogous with Guv,
with which spacetime curvature is computed.

To highlight that problem, consider the relation of power
(which is quantized) to the metric "g_00" in the "Marsh-
Mellow" gedanken here,
http://physics.trak4.com/MST_UFT.pdf
What do you think?

Well I think we should be able to solve the problem
either way, and then get a fusion of technique.

> Regards
> Charles Francis
> http://www.teleconnection.info/rqg/MainIndex
Cheers
Ken S. Tucker

[Ken S. Tucker]

Hi Mr. Masse et al.

On Aug 10, 7:31 am, "Cl\.Massé" <danielle.be...@gmail.com> wrote:
> "Shubee" <e.Shu...@gmail.com> a écrit dans le message denews:2a7a0dc4-6dfc-40a9...@2g2000hsn.googlegroups.com...
>
> > "A great physical theory is not mature until it has been put in a
> > precise mathematical form, and it is often only in such a mature form
> > that it admits clear answers to conceptual problems." A. S. Wightman,
> > Hilbert's sixth problem: mathematical treatment of the axioms of
> > physics, in: Proc. Sympos. Pure Math., Vol. 28, AMS, 1976, pp.
> > 147-220.
>
> > Don't you believe that coming up with "clear answers to conceptual
> > problems" is being productive?
>
> I don't think the issue is "precise mathematical form", but rather
> "convenient mathematical form", for it would mean that the physicist are
> imprecise, which is obviously wrong. Even if the mathematical formulation
> lacks rigor, it precisely and consistently describes what is observed, and
> it is the only goal.
>
> It often takes years before the theory is conveniently formulated and
> spelled out in textbooks. The convenient mathematical form is the one based
> on a minimal set of conceivable and insightful postulates. But again, it is
> a physical task, and not a mathematical one.
>
> > Mathematicians have no problem understanding the meaning of
> > mathematics. Perhaps physicists should try to reduce physics to
> > mathematics.
>
> There is nothing to understand in the meaning of mathematics. Either a
> theorem is true, either it isn't, period. It would be like trying to
> understand true & true = true. It's no news that the mathematicians
> consider the physicist as sort of backward people. But the truth is that
> both disciplines can't be compared since they have very different purposes
> and philosophical status.

Your last paragraph troubles me, because I think
logic is a discipline, and mathematicians I've met
have always respected the applications of math.
Let me provide an enigmatic example.

Let a vector A have components A_u and set a
covariant derivative (w.r.t "w") as,

(A_u A_v);w = 0 , (1)

which is symmetrical in indice "u" and "v".
Next, watch this, I'll expand Eq.(1) via elementary
*chain rule* to,

A_u;w A_v + A_u A_v;w = 0 meaning

A_u;w A_v = - A_u A_v;w , (2)

where Eq.(2) is asymmetrical in "u" and "v".

((That is important for me because I want to generalize
Eq.(GRCC2) in this article,
http://physics.trak4.com/GR_Charge_Couple.pdf
with the covariant derivative of the metric vanishing)).

How can both identical Eqs.(1) and (2) be the same,
and be symmetrical and asymmetrical?

((J. Baez in week 268 discusses this,
"g(ab,c) = e(a ^ b ^ c) = g(a,bc)
So, it works! But, this algebra is far from semisimple." )).

Based on mathematics, I reason both sides of Eq.(2)
vanish, for both Eqs.(1) and (2) to be consistent.

But I'm still without an effective solution, so I do a bit
of physics induction, as a shot into the math, and
reconstruct Eq.(1) as,

(A_u B_v);w =0 , (1A)

wherein indice "u" and "v" can be asymmetrical, and
A and B are *different* vectors enabling,

A_u;w B_v = - A_u B_v;w , (2A).

Eq.(2A) is very rich, nonsymmetrical in vectors A and B,
and indices "u" and "v".
Once again though, Eq.(2A) will a need a shot of physics
to hone it down to apply more easily in the universe we
inhabit, by the discipline of physics, to distinguish it from
the infinity of universes mathematicians can logically define
and inhabit.

[Ken S. Tucker]

Fred, get out the spatchula, we'll need to
scrape Jay off the ceiling...again.

On Aug 10, 8:45 pm, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:
> On Aug 10, 8:27 pm, "FrediFizzx" <fredifi...@hotmail.com> wrote:

> > "Jay R. Yablon" <jyab...@nycap.rr.com> wrote in messagenews:daed5371-67e3-48c3...@k13g2000hse.googlegroups.com...
>
> > > There has been a fair amount of discussion these several weeks about
> > > zitterbewegung, the velocity operator, Foldy-Wouthuysen
> > > transformations, and many other questions. Three things strike me
> > > as
> > > important about this discussion. First, there is not any real
> > > agreement among our sci.physics.foundations participants about these
> > > questions. Second, I would submit that even the professional
> > > physics
> > > community is not of a single mind about these questions. Third –
> > > and
> > > I believe the source of the foregoing – these are open research
> > > questions to which, I will humbly submit, definitive answers are
> > > still
> > > elusive.
>
> > Particle physicists that follow the Standard Model (SM) for such
> > questions most likely have a single mind about this. Zitterbewegung
> > is quite compatible with the SM. Fermions have no mass without an
> > interaction with the Higgs field. IMHO, zitter is from the
> > interaction with a Higgs-like field which probably has its own zitter.
>
> Hi Fred,
>
> That is the first completely sensible explanation I have seen of how a
> fermion could be "temporarily" and instantaneously massless and
> luminous. By this explanation, one could say that we had the first
> signs of interactons mediated by discrete boson exchanges shortly
> after Dirac's eqaution was first discovered.
>
> > When you see m in the Dirac equations it can easily be replaced by
> > 2pi/L_C, compton wavelength, or hbar w_C. IOW, replace mass with
> > energy in the Dirac equation.
>
> Yes . . .
>
>
>
> > > At the link below, I sketch out may be the solution to all of this,
> > > namely, that quantum gravitational fluctuations are responsible for
> > > the precise cancellation of the predicted zitterbewegung and its
> > > attendant luminous movement by massive particles, resulting in the
> > > state of affairs in which the zitterbewegung is simply not observed.
>
> > The fundamental issue here is does a fermion have a "local" "at rest"
> > frequency of w_C? Compton Shift indicates that it does so I am not
> > sure why someone would think that zitter is not observed indirectly.
>
> Well, is it or isn't it? That is an experimental question. I seem to
> have seen pretty strong views expressed here that is isn't.
>
> > It is not directly observed because the frequency is too high for our
> > current measurement capabilities.
>
> I am not sure about his last statement. The electron has a mass of .
> 511 MeV, or if you like, corresponding Compton wavelength or
> frequency. That is the same, roughly, as the frequency of the
> zitter. We now have TeV accelerators -- a million times more
> energetic than the electron. Do you mean to tell me that we canot
> resolve electron oscillations or frequency time frames on the order of
> 1MeV with an available TeV capacity? Do we have to drop an electron
> into the "big bang" to resolve this? ;-)
>
> I have spent a month or more working form the supposition that there
> is a zitter, and now I am entertaining some pretty strong statements
> on this group that there is no zitter, and I really would like an
> answer one way or another.
>
> Notwistanding, and not to be waffling, I can accept either answer.
> But, if there is a physical zitter, and if it is on the order of the
> Compton wavelength, then I do not see how one would ditinguish the
> zitter from the wave behavior of the electron which is also on the
> same frequency order. These must be one and the same. Zitter = wave
> properties of matter. And, as I said before, FW tranformation is a
> tranformation between the dual "wave" and "partcile" properties of
> nature. I could be perfectly content with that view.
>
> On the other hand, if there is not a zitter, then one must explain how
> this is to be so given Dirac's equation. Sweeping it under the rug
> with a FW transformation does not really cut it because you cannot
> change the observed physics by a unitary tranformation. The best you
> can do is simplify certain expressions (including finding that some
> operator expressions mirror their classical counterparts) and at the
> same time complicate other expressions (especially when there is a
> gauge field), and maybe gain a little better understanding.
>
> I would like especially to get some review of my eqaution (6) and
> whether this is or is not a problem to have the mass itself start to
> zitter which is what that equation suggests once unitary quantum time
> evolution is considered. Remember, if the mass zitters, then so does
> the compton wavelength and the frequency. Notwithstanding what you
> said before about Higgs which is a quite ingenious argument, am I
> wrong to be concerned that (6) implies a mass zitter (on top of all
> the other zitters), and ought one be concerned enough about this to
> therefore use an equation such as (10) to try to avert the rest mass /
> wavelength / frequency zitter?
> Best,
> Jay.

Hi Jay
((I think there's a minor typo in your (14) where sigma
and rho is concerned)).

Off hand, Eq.(13) looks geodesical, the R.H.S. *looks*
like what a Christoffel might appear as. As you know,
a Christoffel is not a tensor, and I suggested awhile ago
that the Hamiltonian can be made to vanish in GR, but
OTOH, Reiman Curvature is founded on Christoffels,
that's the RC tensor, (IIRC) and Christoffel's aren't
tensors.
I presume your summation on index "k" therein is 4.
Ken
PS: I was wondering how that R.H.S. relates to g-waves?
With the LIGO appartus up and running, any thoughts on
how vierbein e^0_0 could be measured?

[Ken S. Tucker]

Hi Fella's, some commetary below...

I came into the problem of Eq.(1) and (2) above entirely
open minded but the mathematical contradiction fed-
back into the theory and my understanding of physics.

There is an ongoing controversy about fields reacting
with themselves, such as a charge "self-energizing",
but the *mathematical* contradiction/enigma above
compelled me to re-examine that notion.

The Eqs.(1) and (2) above, using the discipline of tensor
analysis, has NO logical solution, that I know of,
therefore I was compelled to solve the problem by
using interacting charges, extended to A and B
below in Eq.(1A) and (2B).

Well that rendered another problem...
Our friendly mathematicians designed tensor analysis
to analyse static curved surfaces in N-dimensions.
Einstein and his buddy's took that math into a
dynamic spacetime, which I can describe here,
http://physics.trak4.com/modern-spacetime.pdf
compatible with our common definition of the meter,
so that looks ok.

Then the next problem, defining distance in a curved
spacetime. As it happens, using EFE's provided a
simple solution, see Eq.(4) herein...
http://physics.trak4.com/GR_Charge_Couple.pdf
and please examine Eq.(4) to find the differentials.

S dS = X dX

and the increments

S DS = X DX

are both true, to permit either a continuum (dS) or a
quantized solution (DS) respectively, extended from
the Orthogonal quantities X, dX and DX, since those
later values are in linear proportion.

It's my opinion and respect of the EFE's that they
provide a basis for a continuum and/or quantized
solution, based on the examination above.

Regards
Ken S. Tucker
...

refs

[Ken S. Tucker]

Hi Gals & Guys.

On Aug 12, 12:08 am, neurop...@yahoo.com.au wrote:
> Sir Jay wrote:
> > Ah, Dear Masked Princess, but free Dirac theory is non-interacting
> > in all but one respect. It still contains a rest mass m, and this
> > interacts gravitationally.
>
> If it interacts with anything, then it is not the "free" Dirac theory.
>
> Methinks you mean a Dirac theory in curved spacetime,
> which is a rather different dragon (theory).
>
> ----
> LOL from the MQD as she gallops past in haste!

"Gallops", I have a spare rocket ship to loan out.

I see "mass" and "matter" as quite distinct, where
mass is defined gravitationally and matter atomically
by EM, of course Strong and Weak force can be
part of the definition of matter if one chooses to hold
them distinct from gravity and EM.

It's a proven fact that GR converts spacetime to mass,
that's what deflection of light measures when 2x more
than Newtonian theory predicts, as is well known.

If GR is to be respected, then mass is a spacetime
effect, then deBroglies "mc2 = hf" requires "f" to be
inseparable from the spacetime field.

It is the understanding of how to transform mc2=hf
that provides difficulties, (for me).
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Chalky and friends...

On Aug 13, 5:12 am, Chalky <chalkys...@bleachboys.co.uk> wrote:
> On Aug 10, 9:45 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> > Newton's laws are themselves the axioms.
>
> Yes, and the axioms were deduced logically from observation.
>
> > We do not derive axioms
> > mathematically, but rather all mathematical proof must proceed from
> > axioms. The mathematical challenge is to establish precisely the axiom
> > set which yields a good model of physics.
>
> Yes, IE good correlation with observation
>
> > Newton, Einstein, and Maxwell
> > have made the most important contributions to physics because this is
> > what they did.
>
> Well, in terms of applied physics, at least, I would have said that
> Faraday's contribution was as great as Maxwell's. Maxwell's equations
> gave us radio (via Marconi) and TV (via Baird) Faraday gave us
> electric motors and dynamos,hence the electric grid, and Faraday's
> education in mathematics and logic was limited to what he learned at
> Sunday school.

An electrician friend of mine, maintained a paper
mill, and would hire new engineers. Well the new
engineer would argue the "book" says bla-bla-bla,
but the friend would counter, "machinery can't read".

Same thing applies to the universe.
The people you cite I would regard as theoreticians.
Just about anyone can memorize the "book" and
be "book smart", but very few can add a page to
that book.

A theoretician is then a technician who employs
mathematics, (and mathematicians) , but those
guys knew the book, and what was important and
sidelined the obvious trivial dogma.

A guy like Newton actually built and invented the
Newtonian reflector telescope by grinding and
polishing his own mirrors etc...those guys were
hands-on people.

So instead of arguing mathematics vs physics
or mathematician vs physicist, we should see
how the eclectic skills of a theoretician evolve.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Dr Enders, a bit OT, but you tickled my brain...

On Aug 13, 5:26 pm, Peter <end...@dekasges.de> wrote:
...
> Mathematical equations express both quantitative and qualitative
> relationships. The latter is often specific to the discipline where it is
> applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
> necessary, but, nevertheless, auxiliary part of a natural science.

Interesting, photosynthesis...

photon + plant + CO2 => plant + C + O2

Is the weight of C apart from O2 greater than the weight
of CO2?

I think it is because,

C + O2 => CO2 + heat , heat = mc^2.

That's important if you heat with wood, and a very nice
example of how solar fusion using E=mc^2 produces
photons, that are then converted to m=E/c^2 via plants,
to grow trees.

Thanks Peter, better than a cup of coffee.

I'm always interested in a way of finding m=E/c^2
demonstratably, and pair production of taking a
gamma to a positron+electron is fairly hi-brow.

Of course it would be nice to build a solar powered
machine that splits CO2 and H2O neatly and spits
out C8H18 (octane?)...maybe nuclear powered...
Regards
Ken S. Tucker
[snip agreeably]

[Ken S. Tucker]

Hi Murray and all.
[...]

On Aug 14, 8:05 am, ar...@iname.com (Murray Arnow) wrote:
> Peter, this isn't a voting issue. One may say it's a historical accuracy
> issue, but I say it's a matter of courtesy. It is discourteous to quote
> a person without identifying him.

I certainly agree. I designate a snip using ... or [...]
or [snip] with a comment. That is to abbreviate the
thread and of course one may return to find what
was snipped. Sometimes a poster might find his
important stuff snipped, so they can reinsert it.

Also, I try to designate the primary person(s) I'm
directing my comments to. Perhaps we should
set-up some guidelines to follow for courtesy but
then we also have persons who have an artistic
poetic style that is fun too.

> You haven't been singled out on this. I am seeing others no longer
> attributing posts. Maybe the moderators can gently remind posters to
> include the attributions.
> Murray

Back to math-physics. I've been admiring your
(and all) philosophy on that subject.
Allow me to present a problem (I sometimes get
ridiculed on :-( ).

In GR the rate of time is "mathematically" defined
at a point by the metric g_00, however in 1983
a finite length and time were "physically" interdefined
using "c". Even looking at the functioning of a Cs
atomic clock, a small finite length is required to
establish the time rate, so physically "g_00" is
defined by a finite length, but mathematically at
an infinitesmal point.
That is a heck of a difference, because the "physical"
definition compells a "quantization" of the tensor
analysis used in GR, which I privately find is doable,
and posted the elementary procedural approach in a
thread in this group, "Flat/Curved SpaceTime", but
it was mocked so I quit the thread. Of course I
learned to improve the reasons for why to do it,
so the criticism was very helpful, and I may add the
complete analysis to my web site here,
http://physics.trak4.com/
that deals with the Modern SpaceTime revision of
1983.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Dr. Enders

On Aug 15, 1:51 pm, Peter <end...@dekasges.de> wrote:
> In order to avoid misunderstandings in several (sub)threads, I would like to
> propose to find a common understanding of certain basic notions, such as
> 'causality'. (For 'locality', see the foregoing new thread.)
>
> To begin with, my understanding of 'causality' is, that an event has got a
> cause.

Quote,"an event has got a cause." needs clarification.

Personally I have been irritated by the lack of a good
definition as to the meaning of "event" in relativity, so
in place of the word "event" I'll use "occurance".
((I've replaced the usual spelling of occurence)).

Within a finite volume DV = DxDyDz, is a detector or
an emitter, able to measure an incremental change of
Energy in a finite interval of time, DE/Dt = Power.

I think that the term "occurance" is a quantization
of the word "event", where event is presupposed to
be able to occur at a point, which is unrealistic.
Mathematically, let Occurance (o) be defined,

(o) = DV Dt DE.

((I'm using bracket's around "o" so we don't confuse it
with zero and because it is has a finite spacetime
volume)).

With OCCURANCE (o) defined we can examine and
define "causality", as a relation between two (o)'s,
such as the emission and subsequent absorption
of a photon, "~~~~",

(o) ~~~~~~> (o')

and (o) = -(o') defining causality.

I think "casuality" is another term for Conservation
of Energy, but I'm having problems with understanding
Power, which appears to be Energy Flow or IOW's
Energy Flux.

I'll stop here pending suggestions and/or approval.
Regards
Ken S. Tucker

> The principle of causality states that *all* events have got a cause ('nihil
> sine ratione', as Leibnitz said).
>
> This 'obvious truth' or 'necessity of thinking', as some may said, was
> obscured by unlucky historical developments. It was incorrectly connected
> with classical-mechanical motion. Quantum mechanics has revealed that such
> motion does not take place within atoms. Unfortunately, not only the
> classical-mechanical motion was rejected, but also causality in general. This
> confusion seems to endure to our days...
>
> Thus, I would like to agree with you, that causality is a universal
> principle, where the concrete form of realization depends on the specific
> area of application.
>
> Of course, this is just an initial sketch -
>
> Looking forward,
> Peter

[Ken S. Tucker]

On Aug 16, 3:30 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
>
>

> >Hi Dr. Enders
>
> >On Aug 15, 1:51 pm, Peter <end...@dekasges.de> wrote:
> >> In order to avoid misunderstandings in several (sub)threads, I would like to
> >> propose to find a common understanding of certain basic notions, such as
> >> 'causality'. (For 'locality', see the foregoing new thread.)
>
> >> To begin with, my understanding of 'causality' is, that an event has got a
> >> cause.
>
> >Quote,"an event has got a cause." needs clarification.
>
> >Personally I have been irritated by the lack of a good definition as to
> >the meaning of "event" in relativity, so in place of the word "event"
> >I'll use "occurance". ((I've replaced the usual spelling of
> >occurence)).
>
> >Within a finite volume DV = DxDyDz, is a detector or an emitter, able
> >to measure an incremental change of Energy in a finite interval of
> >time, DE/Dt = Power.
>
> >I think that the term "occurance" is a quantization of the word
> >"event", where event is presupposed to be able to occur at a point,
> >which is unrealistic. Mathematically, let Occurance (o) be defined,
>
> >(o) = DV Dt DE.
>

> Event just means a space-time coordinate. It should be implicit that a
> space time coordinate is something measured, and equally it should be
> implicit that measurement is to within error bounds.

Exactly, those "error bounds" import HU,
(Heisenberg Uncertainty). I purposefully built
that in by using DV3=DxDyDx and DV4=DV3*Dt
to account for those boundaries, but my entry
into the subject was gentle.

For example, suppose Planck's "h" expressed in
Ergs Seconds is the eqivalent of (h= DE Dt) and
DV is invariant, then (o) is invariant.
((Fred, please see Spiegel, pg.203..66 and find
dV=dV' as invariant)).

((I'm uncertain my reasoning is entirely valid))

Next, DV3*h = invariant = (o).

Once the "occurance's" themselves are defined
invariantly, then the differences of the (o)'s above
are mathematically invariant.

Let's presume Tucker's reasoning is close.
If so, we find a means to define "casuality"
Generally Covariantly.

That is why I think Dr. Ender's question is important,
that I'll rephrase as, "Can Casuality be expressed as
a law of physics", true w.r.t all CS's?

> In relativity, I
> don't see a problem with modelling coordinates using a continuum.

Well I certainly do, and cared enough to formulate
and provide a rework of the sematic "event" to give
a (fairly) clear invariant definition of "occurance",
compatible with QT, QM.

> The
> problem starts to arise in quantum theory, when we cannot do the
> measurement even in principle (without fundamentally changing the
> situation).

Well of course, that's why we need to take fuzzy
semantics to hard core paper definitions.

[Ken S. Tucker]

Hi Murray and fellow theoreticians.

On Aug 18, 5:50 am, ar...@iname.com (Murray Arnow) wrote:
> "Ken S. Tucker wrote:
> >To "Y" and Murray...
>
> >Murray Arnow wrote:
> [...]
> >> A major problem in physics is the requirement of functional definitions.
>
> >LOL, that's not a problem...that's a solution!
> >95% of my problem is figuring out that "functional
> >definition".
>
> I wish to state a correction: I should have used the more common
> terminology "operational definition" rather than "functional
> definition." I chose not to write an immediate correction knowing that
> the people here would understand the meaning; however, I don't think it
> wise to continue using a less familiar term.
>
> Back to Ken: If this is a solution, it is an unsatisfactory one.

*An unsolved problem is a wasted solution*, IOW's the
recognition of a problem evolves solutions. The precision
of the "operational definitions" is evolving.

>It gives
> philosophers headaches and new physics students the heebie-jeebies.
> Pragmatically it works, but I'd like to know a mathematicians take on
> this.

Have a look at this link (GR1916) and please bookmark it,
http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200...

Recently we have been discussing causality#, and
event. In the provided link is an ambiguous volume Eq.(18).
So in the thread "Causality", I redid Eq.(18) to form a
new invariant, (Occurance), using "D" as a finite increment
symbol,

(O) = Dx Dy Dz Dt DE

permitting finites, to bring GR and QM more in accord.

To do that, we had to redefine the definition of sqrt(g),
done using the most up-to-date agreeable definitions
of spacetime (MST),
http://physics.trak4.com/modern-spacetime.pdf
In parallel calculation , Planck's "h" needed to remain a
scalar invariant, in accord with physical understanding,
derived empirically.

This may interest you,

If D=>0, D=>d therefore, (O)=>(o), thus

(O) = Dx Dy Dz Dt DE => (o) = dx dy dz dt dE

That enables the recovery of QM's "(O)" expressed
in a continuum limit given by "(o)", mathematically.

Regards
Ken S. Tucker

# I mispelled causality as casuality previously,
by reversing US and SU, it happened during the
cold war as a head injury, I obtained a dyslexia,
mixing up United States and Soviet Union.

[Ken S. Tucker]

Hi James and all.

On Aug 18, 4:46 pm, jamesfen...@gmail.com wrote:
> On Aug 18, 10:18 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:

> > > In fact, and anyone feel free to chime in on this and set me straight,
> > > but my understanding is that the Heisenberg Uncertainty principle
> > > itself stands on very shaky ground. There is essentially no
> > > experimental evidence, that I'd consider conclusive or credible, which
> > > supports it. In order to achieve this, one would need to show that
> > > for a single particle you cannot locate the position and momentum (or
> > > time-energy etc.) within the value of h. You'd need an experimental
> > > setup that could measure sub-h resolution, and then you'd have to use
> > > this on single particles and show, it cannot be done. Statistical
> > > analysis of particle ensembles, as is done now and in all experiments
> > > up to now, is inadequate. In fact, such experiments ignore Einstein's
> > > point that QM is just a probabilitistic statistical theory for
> > > particle ensembles and does not apply to single particles. I
> > > understand that the appropriate experiment is an enormous
> > > technological challenge, but considering the central importance of the
> > > uncertainty principle to pretty much all of physics, it is a surprise
> > > that it has almost no experimental support. For a recent paper
> > > discussion the lack of experimental evidence for the Uncertainty
> > > Principle seehttp://philsci-archive.pitt.edu/archive/00003077/01/UR_BHL2006.pdf.
> > > I find this shocking.
>
> > I'm working on a similiar problem, *what is the limit
> > of accuracy of a clock?* , such a question involves
> > the uncertainity of a time measurement.
> > Some find "Planck Time" to be that limit, however
> > here's a pop-sci link, doing experiments on that,http://www.space.com/scienceastronomy/quantum_bits_030402.html
> > that claim to shed doubt on many fundamentals.
> > Regards
> > Ken S. Tucker- Hide quoted text -
>
> > - Show quoted text -
>
> That pop-sci article is very interesting! I too have been amazed at
> the clarity of the Hubble Ultra Deep Space images, but it never dawned
> on me that they should be blurry, but of course they should be. How
> interesting. Well I'm happy to see others are doing this type of
> research, including you and those mentioned in this article. There is
> no better test tube or experimental apparatus than the whole universe
> now is there?

A comment on pop-sci. There is some hype, but
science needs to compete against Hollywood,
sports, politics, the economy and so forth, and
the article provides leads to the basis papers.
When a string-bean basket ball player throws a
long ball for a sink, the world cheers, that's fine,
but when NASA tosses a satellite and takes a
picture of the far side of Uranus, a lot of people
think using a mirror is easier :-).

Seriously now: The suggestion from the article
splits QT (Quantum Theory) from the mathematically
evolved QM (Quantum Mechanics), that suggests
light follows a path with a random (probabilistic)
element, that we see is NOT evident.

Allow me to speculate a bit:
If a clock of infinite accuracy is theorized, then
something must propagate at an infinte rate !?!.

If the maximum rate of propagation is finite, for
example "c", then the accuracy of a clock is
finite.

If the accuracy of a clock is finite, then time and
length have a limit to their measuring resolution,
that we may call "uncertainty".

That "uncertainty" is defined using Plancks "h",
so it follows we should be able to relate "c" and
"h" from the same principle, maybe unit spin ??

The reasoning appears superficially valid, but I'm
short on hard core proof.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Dr Enders, Charles, Murray and all.
(also someone called "Y"...ugh)

On Aug 19, 6:21 am, Peter <end...@dekasges.de> wrote:
> > Y wrote:
> > >The Rule : Every Structure has a foundation.
>
> > >Introduction
>
> > >Let us assume then that we have limited our recording capaity using
> > >quantum computers and three new units have come into being. These
> > >units are almost already into being and at current our technology
> > >supports down to approx 3 Atoms per bit, or .333 bits per atom.
>
> > >These units are - Bits/Atom Digit/Atom and Symbol/Atom
>
> > >This means Bits per Atom, Digits per Atom and Symbol Per Atom. You
> > >see, just like our MP3 files which record music at 197Kilobits per
> > >Second, we must not forget that the MP3 file also has a mass.
> > >According to my Hard drive on a clunkier technology which weighs .6kg
> > >ang contains 2781197205504 bits a bit has a mass of 2.15 X 10^(-13)kgs.
>
> > >As an architect, I am accustomed to the fact that my ruler, i.e. the
> > >thing I am measuring with has a mass. If we were to count seconds with
> > >a machine, we would also require a certain mass in order to keep
> > >count, just like our ancient abacus beads.
>
> > >The Equation.
>
> > >Eternity = Mass(universe) / Mass (Unit of record or the SI unit)
>
> > [snip material much too profound for my understanding]
>
> > The moderators have
>
> Actually, one of the moderators has...
>
> According to our group charter, a posting should be passed, if one of the
> (currently, four) moderators votes for passing. If the first moderator who
> checks a posting finds it in agreement with the charter, he approves it
> without asking his fellows co-moderators.
>
> I agree, that formulations like "This means Bits per Atom, Digits per Atom
> and Symbol Per Atom. You see, just like our MP3 files which record music at
> 197Kilobits per Second, we must not forget that the MP3 file also has a
> mass...", say, sound unphysical.
>
> On the other hand, we moderators are happy to promote novel ideas. And here,
> the border to unphysical speculations is not always clear.
>
> We moderators welcome comments of this kinds as they help us better to judge
> the expectations of the group members :-)

I'm glad you passed Y's post.
It relates to Charle's post about radioactivity (decay
rates) in the "Casuality" thread, and I'd like to link
them via a confusion I'd like to share about Neutron
(n) decay rates when (n) is free and unbound to a
nucleus, and that is ~ 15 minutes of life time, from
tables.

Well, as a brat I'm reading along studying mean
lifetimes of meson and hyperons seeing 10^-10 secs,
and my brain screeches to a halt at the (n) life of
15 minutes, which is like a relative eternity!

Next, how can a tiny thing like a (n) contain some
sort of clock that ticks off to explode in ~15 minutes??
If anyone wishes to explain how that sort of timer
can be contained within the (n)'s structure I'd be
happy to read about it.

So Tucker goes over to causality theory using
neutrino flux to explain the (n) decay rate, it's
obviously a fringe notion due to lack of data.
Let's begin with a quiki wifi, for ref,
http://en.wikipedia.org/wiki/Neutron
and see the (n) decay as,

n => p+e+v'

and do a causal reversal to

n+v => p+e

with the neutrino (v) being of the appropriate
energy to intiate the (n) decay, thereby laying
radioactive decay rates on the (v) flux.

That was all conjecture until Super Nova 1987a.

Reports came in of a large amount of (v) flux from
terrestrial detectors and a star nearby SN1987a
brightend.
I'm sorry I cannot find an immediate ref to that
nearby star, the phenomena was fleeting,
however, if the observation was true, then the
(v) flux accelerated the *rate of fusion* within the
nearby star, and so to the rate of radioactivity,
that resulted from the (v) pulse from SN1987a.

That provided the 1st evidence that decay rates
are proportional to neutrino flux, hence providing
a causal basis for neutron decay life times.
...

> > It is certainly a
> > major problem with Newton's force laws (force and mass can not be
> > defined independently).
>
> Not necessarily. The force between two charged bodies can be measured without
> reference to mass using a torsion scale (Coulomb 1785), when the scale is
> gauged independent of mass.
>
> > And time is of course something that is a real
> > bear to define. A discussion about this would may prove worthwhile.
>
> Is there an alternative to periodic processes?
>
> Thank you,
> Peter

Best Regards
Ken S. Tucker

[Spaceman]

Ken S. Tucker wrote:
> I'm glad you passed Y's post.
> It relates to Charle's post about radioactivity (decay
> rates) in the "Casuality" thread, and I'd like to link
> them via a confusion I'd like to share about Neutron
> (n) decay rates when (n) is free and unbound to a
> nucleus, and that is ~ 15 minutes of life time, from
> tables.
>
> Well, as a brat I'm reading along studying mean
> lifetimes of meson and hyperons seeing 10^-10 secs,
> and my brain screeches to a halt at the (n) life of
> 15 minutes, which is like a relative eternity!
>
> Next, how can a tiny thing like a (n) contain some
> sort of clock that ticks off to explode in ~15 minutes??
> If anyone wishes to explain how that sort of timer
> can be contained within the (n)'s structure I'd be
> happy to read about it.

Simple classical view here for you.
(I will speak of gears of course.. cause I am a gear head.)
It is actually a matter of imbalance and external forces
that effect the imbalance.
The larger the imbalance, the faster it will break apart.
The smaller the imbalance, the longer it will stay together.
If there is no balance problem at all, it will spin as one, until
something creates an imbalance to it.
Balance is also subject to external forces also.
A gear that is not balanced and not pushing against
anything else can hold together longer than a gear
that is not balanced that is turning another gear.
An imbalanced gear that has no external gear forcing
it to remain in place will find the center of gravity for the
imbalance and the gear will not break up as quickly
because the center of gravity will move to balance
the imbalance problem when not forced upon another gear.
If the imbalanced gear is force to not be able to allow
a change of position of it's center of balance, it will break apart
faster.

--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
Spaceman

[Ken S. Tucker]

On Aug 19, 11:16 am, "Spaceman" <space...@yourclockmalfunctioned.duh>
wrote:

> Ken S. Tucker wrote:
> > I'm glad you passed Y's post.
> > It relates to Charle's post about radioactivity (decay
> > rates) in the "Casuality" thread, and I'd like to link
> > them via a confusion I'd like to share about Neutron
> > (n) decay rates when (n) is free and unbound to a
> > nucleus, and that is ~ 15 minutes of life time, from
> > tables.
>
> > Well, as a brat I'm reading along studying mean
> > lifetimes of meson and hyperons seeing 10^-10 secs,
> > and my brain screeches to a halt at the (n) life of
> > 15 minutes, which is like a relative eternity!
>
> > Next, how can a tiny thing like a (n) contain some
> > sort of clock that ticks off to explode in ~15 minutes??
> > If anyone wishes to explain how that sort of timer
> > can be contained within the (n)'s structure I'd be
> > happy to read about it.
>
> Simple classical view here for you.
> (I will speak of gears of course.. cause I am a gear head.)

My Old Boy was mechanically inclined, he was
a pretty sharp fella.

> It is actually a matter of imbalance and external forces
> that effect the imbalance.
> The larger the imbalance, the faster it will break apart.

So that's like a vibration that becomes
destructive?

> The smaller the imbalance, the longer it will stay together.
> If there is no balance problem at all, it will spin as one, until
> something creates an imbalance to it.
> Balance is also subject to external forces also.
> A gear that is not balanced and not pushing against
> anything else can hold together longer than a gear
> that is not balanced that is turning another gear.
> An imbalanced gear that has no external gear forcing
> it to remain in place will find the center of gravity for the
> imbalance and the gear will not break up as quickly
> because the center of gravity will move to balance
> the imbalance problem when not forced upon another gear.
> If the imbalanced gear is force to not be able to allow
> a change of position of it's center of balance, it will break apart
> faster.

Funny that a neutron is stable within the
nucleus. I wonder if it stabilizes by the
strong nuclear force when "geared" to a
proton.

> --
> James M Driscoll Jr

Regards
Ken S. Tucker

[Spaceman]

Ken S. Tucker wrote:
> On Aug 19, 11:16 am, "Spaceman" <space...@yourclockmalfunctioned.duh>
> wrote:
>> Ken S. Tucker wrote:
>>> I'm glad you passed Y's post.
>>> It relates to Charle's post about radioactivity (decay
>>> rates) in the "Casuality" thread, and I'd like to link
>>> them via a confusion I'd like to share about Neutron
>>> (n) decay rates when (n) is free and unbound to a
>>> nucleus, and that is ~ 15 minutes of life time, from
>>> tables.
>>
>>> Well, as a brat I'm reading along studying mean
>>> lifetimes of meson and hyperons seeing 10^-10 secs,
>>> and my brain screeches to a halt at the (n) life of
>>> 15 minutes, which is like a relative eternity!
>>
>>> Next, how can a tiny thing like a (n) contain some
>>> sort of clock that ticks off to explode in ~15 minutes??
>>> If anyone wishes to explain how that sort of timer
>>> can be contained within the (n)'s structure I'd be
>>> happy to read about it.
>>
>> Simple classical view here for you.
>> (I will speak of gears of course.. cause I am a gear head.)
>
> My Old Boy was mechanically inclined, he was
> a pretty sharp fella.

Something about gears and levers and fulcrums etc.
makes people learn a lot about motion and forces.
:)

>> It is actually a matter of imbalance and external forces
>> that effect the imbalance.
>> The larger the imbalance, the faster it will break apart.
>
> So that's like a vibration that becomes
> destructive?

Exactally.
:)
Too much shaky make too much breaky.
:)

>> The smaller the imbalance, the longer it will stay together.
>> If there is no balance problem at all, it will spin as one, until
>> something creates an imbalance to it.
>> Balance is also subject to external forces also.
>> A gear that is not balanced and not pushing against
>> anything else can hold together longer than a gear
>> that is not balanced that is turning another gear.
>> An imbalanced gear that has no external gear forcing
>> it to remain in place will find the center of gravity for the
>> imbalance and the gear will not break up as quickly
>> because the center of gravity will move to balance
>> the imbalance problem when not forced upon another gear.
>> If the imbalanced gear is force to not be able to allow
>> a change of position of it's center of balance, it will break apart
>> faster.
>
> Funny that a neutron is stable within the
> nucleus. I wonder if it stabilizes by the
> strong nuclear force when "geared" to a
> proton.

The proton is more than likely the balancing
"gear" always spinning on the lighter side and both being
held together by outer "gears" of course without
the teeth that is.(surrounding particles and smaller stuff)
It's all ratios, circumferences and pressure.
Really simple stuff right?
:)

--
James M Driscoll Jr

[Ken S. Tucker]

On Aug 19, 8:42 pm, "Spaceman" <space...@yourclockmalfunctioned.duh>

We had a family hobby of building tracked
vehicles, chains, pulleys, levers, good stuff.

> >> It is actually a matter of imbalance and external forces
> >> that effect the imbalance.
> >> The larger the imbalance, the faster it will break apart.
>
> > So that's like a vibration that becomes
> > destructive?
>
> Exactally.
> :)
> Too much shaky make too much breaky.
> :)

Well then somehow a (n) must have states
that causes it to blow in 15 minutes.
How could you describe the (n) so it can
do that?

Not sure if the gear analogy holds, but it's
worth a look.
Ken

[Spaceman]

Hmm, 15 minutes and then poof, it throws off
a negative electron and antineutrino and becomes
a stable proton
so when it leaves it becomes a three "parts"
unstable balance problem.
Well I will again think of "gears" but of course
they don't have teeth and act more like wheels
the center part would of course be the most massive
wheel and the proton and the two imbalanced parts
would be the electron on one side and the antineutrino
on another side.
opposite each other but the long time seems
that they may balance each other out for a while.
If the "gearing" is still held together by external forces
such as other electrons and smaller stuff spinning the
opposite direction to "conserve energy like any gearing system
does naturally.
they may take 15 minutes to race around trying to
catch up to one another and then finally
when one gets close enough. (thinking two gears/wheels
spinning around 1 center gear/wheel,) they will collide and
one gear will jump the other (the gear in back would
actually get knocked outward first since the rolling
motion of the back gear catching up to the forward
gear would cause the forward gear to kick the back
gear and the back gear would tend to want to ride
over the forward gears rolling motion.
when both collide.. bang... the thing blows apart because
the surrounding "stuff" (electrons etc) are just not enough
pressure anymore to keep such a collison from
breaking the balance and pressure that held such
in balance.

Hmm.
what wheel/gear is smaller, the neutrino right?
so the antineutrino would be the smaller gear and the larger
electron gear would be the one that catches up and
finally overcomes it and jumps the antineutrino and
because the electron is spinning fast enough with enough
mass, it forces the surrounding electrons etc. and is able to
escape the pressure that was holding it in place to begin with.
Well.
That is one crazy thought.... but who knows til we can
actually make such a small movie.
:)
And yes I am crazy, but I still know I am not stupid.
:)

It is worth a look, too bad we did nto have a neutrino
microscope yet instead of only that giant electron one so far.

[Ken S. Tucker]

Hi Mr. Driscoll
Nifty essay...

On Aug 19, 9:53 pm, "Spaceman" <space...@yourclockmalfunctioned.duh>

What intrigues me is the way gears may be
used in the reaction you describe because
they are naturally quantized, i.e. you
can't have a gear with 10.5 teeth, it has
to be an integer.
So I read your suggestion as having at least
3 gears (p,e,v') and maybe more in the p.
Ok.
Then - if I understand correctly - when
the gears acquire a certain alignment,
the system explodes. ((Sounds like a one
arm bandit jack-pot deal)).

Well do you think it's possible to actually
specify the number of teeth in each gear?
Maybe you're putting the Mechanic in Quantum
Mechanics!

> James M Driscoll Jr

Cheers
Ken

[Spaceman]

Ken S. Tucker wrote:
> Hi Mr. Driscoll
> Nifty essay...

Thanks.
:)

Well, they don't really need to be teeth,
It could be surfaces such as a wheel would have and
it could still be of course a non integer such as 10.5
since surfaces can still do such ratios.
and of course. as any good mechanic knows
you can't have 3 wheels all touch each other of heat
is created and eventually one will kick another other
out of the way so to be stable you could only have
one "gear/wheel" touch as many as do not allow two
outer wheels to touch each other.
If you take one wheel, and place it in the center,
depending on the size of the next outer wheels you can
place as many as can fit as long as they do not touch the
adjacent gear/wheel in that circular level, as soon as one touches
another, it will either create heat if kept together by outer
forces or the level will force one out or even cause catastrophic failure
of the entire wheel system.

Well, If they leave the mechanics out they might as
well call it "Quantum non physics".
:)
I don' think it would be gears although it may be, but
the surfaces still act like a gearing ratio, but can be smooth
or even gaseous in some cases to still work as a
gearing ratio of some sort".
circumference vs circumference ratios.
friction wheels, sliding etc and maybe even some irradic
type surfaces that have spread out "gears" that allow sliding
and then a kick of a turn.
But there are only so many ways one thing can spin another
(like gears without the actual teeth or with spaced out teeth etc..).
And of course it all does have to follow mechanical laws
of such when it comes to "structure" to still call it mechanics
at all. (quantum or not)

[Ken S. Tucker]

Hi Mr. Driscoll.
Thank for the input.
I'm still partial to neutrino flux.
Ken

On Aug 20, 7:06 am, "Spaceman" <space...@yourclockmalfunctioned.duh>

[Spaceman]

Ken S. Tucker wrote:
> Hi Mr. Driscoll.
> Thank for the input.
> I'm still partial to neutrino flux.

Well,
Flux (if I am thinking the same flux term)
would also be a part of the "wheel" system especially
when (like I do) the wheels can be considered to be high
pressure fronts and low pressure fronts. (like clouds almost)
and the "gearing" of the clouds would also have to account
for "energy transfer" between the clouds for any "touching"
the wheels do.

Like tiny little weather systems around a super tiny
planet.
weather systems that can even be ejected if they overcome each
other. and since they are not too much different than surrounding
spaces (unlike Earth and our clouds compared to outer space)
but still all reacting like "wheels upon wheels upon wheels"
etc..

spinning cloud systems of the tiniest stuff and maybe even
more tiny stuff.
I know that deviding in half.... does not stop mathematically,
so why would we stop "physically" at all yet?

[Ken S. Tucker]

Hi Mike, Peter et al.

On Aug 22, 8:01 am, Mike <mj...@sirus.com> wrote:
> On Aug 22, 4:55 am, Peter <end...@dekasges.de> wrote:
>
>
>
> > > Mike wrote:
> > > > On Aug 21, 10:49 am, Peter <end...@dekasges.de> wrote:
>
> > > > Generally speaking, logics doesn't provide any *physical* content of its
> > > > relations
> > > Are you denying that everything physical is logical? What in all
> > > reality are you suposing to be not logical? Or at what scale of
> > > measurement do things stop complying with logic as we know it?
>
> > You have understand the opposite of what was said, I'm afraid
>
> > Please derive any physical notion, eg, force, from your formalism, after
> > that, we can continue
>
> > Looking forward,
> > Peter
>
> You're kidding, right?

I'm in fair agreement with Peter.

>If I derive the Feynman path integral, then I
> derive all the physics usually derived from the PI. I don't see the
> problem?

I admire your approach, you're among friends :-).
I and Murray have stated attempts like that, however
I needed to derive "fundamental charge" as a integration
constant ( $ 0 dx = q) , which is a static invariant and
then fill in "c" as a maximum rate of change, which is
the dynamic invariant. How can pure logic derive them
and also a fundamental relation of those two invariants?
Have you been able to do that?
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Charles, Harry, Murray et al.

On Aug 22, 8:24 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>

> >"Murray Arnow" <ar...@iname.com> wrote in message
> >news:g8k3f4$p73$1...@e250.ripco.com...
> >> harry wrote:
>
> >>>Since mass can be defined as a single concept (and even has been so in
> >>>classical mechanics), it's not really a requirement but more a convention.
>
> >> It is more than convention. Inertial mass is defined through Newton's
> >> Second Law and is F/a.
>
> >That's a law of motion which became a secondary definition and which is
> >assumed to be in agreement with the classical one described below. Note that
> >more commonly the definition m=p/v is used. Obviously, the use of different
> >definitions carries an inherent risk of diverging results...
>
> We cannot use a different definition from the one given by the IPA. Note
> that this, as all proposed future definitions,
>
> http://en.wikipedia.org/wiki/Kilogram#Proposed_future_definitions
>
> ultimately reduce to a precise statement of your earlier intuitive
> definition "amount of stuff".
>
> >>>Mass was (and still is) often determined with a (gravitational) scale and
> >>>inertial effects have been observed to depend on the amount of
> >>>(gravitational) mass. The equations that have been set up to describe that
> >>>dependency allow to determine(gravitational) mass by means of inertial
> >>>experiments. If such would fail then one could of course fix it by
> >>>defining
> >>>different kinds of mass, but also (and more logical I'd say!) by
> >>>correcting
> >>>the inertia equations and/or the gravitational equations. Note that in
> >>>classical mechanics it was proposed that mass corresponded to "amount of
> >>>stuff"
>
> >> That is a high school definition.
>
> >It's an old definition, and it still pops up in the kind of science disputes
> >that I mentioned below. Regretfully it's insufficient in the modern context,
> >as I specified there.
>
> It may be insufficient, but only because it is imprecise. However, it is
> still the basis of the definition of mass, and with good reason. Mass is
> a fundamental, whereas force is not.

The term "fundamental" is ambiguous. Mass, time
and length are *relative* though the quantities "c",
(speed of light in a vacuum), "q" (fundamental charge)
and "h" (Planck's) are usually considered as *invariant*,
(which I agree with).
Which is more fundamental than the other? :-).

I find a need to sub-divide the definition of mass into
two separate catalogies 1) Theoretical, 2) Practical.

For theoretical purposes I needed a definition compatible
with Modern SpaceTime, QT's "h" and relativity based
on the invariant "q" and the time standard, as length is
based on the time standard, for the *rest* (lab) mass,
(It's only 1 page)...
http://physics.trak4.com/MST_Mass-Definition.pdf

The so-called "amount of stuff" solution for the practical
"lab standard" of mass falls into the practical catagory,
and is not a definition mass and energy, it merely divides
the definition of mass into smaller quantities, but then
we're left with defining that atom's mass theoretically
into components relating other basic units like the sec.

I think we'll need to unify the theoretical and practical
definitions of "rest mass". The theoretical definition I
use (linked above) is akin to the electron volt, (ev), but
it's hard to weigh ev's!

> It is a nonsense to define mass in
> terms of Newton's second law..
>
> >> Coming back to my question. How axiomatization of physics affect the
> >> need or use of operational definitions?
>
> >Although I'm not really into that issue, here's my 2cts: as physics is more
> >than the sum of math and logic, by the use of axioms you cannot escape the
> >need for operational definitions.
>
> Einstein, in sr, gave us an excellent archetype. The operational
> definitions are the basis from which axioms are abstracted for the
> mathematical structure.

Yeah, it's more complicated than a chain of deduction,
it's more like fitting triangles together.

[Ken S. Tucker]

Hi Mike and fella's.

On Aug 22, 11:55 am, Mike <mj...@sirus.com> wrote:
> On Aug 22, 12:27 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
...

> > I admire your approach, you're among friends :-).
> > I and Murray have stated attempts like that, however
> > I needed to derive "fundamental charge" as a integration
> > constant ( $ 0 dx = q) , which is a static invariant and
> > then fill in "c" as a maximum rate of change, which is
> > the dynamic invariant. How can pure logic derive them
> > and also a fundamental relation of those two invariants?
> > Have you been able to do that?
> > Regards

> > Ken S. Tucker- Hide quoted text -
>
> > - Show quoted text -
>

> Not yet. I suspect that such constants will only be recognized in
> relation to each other, and not derived separately. I also suspect
> that things like the speed of light will not be derived until the
> particle math is connected to the metric math, in other words, not
> until QM and QG are united. Thanks for the encouragement.

My pleasure. Anyone who takes a serious shot at
such a tough and obscure problem as you demo at
your web-site and calculations has my respect!

> PS. Do you have a link to your efforts?

Yes, Fred and I assembled this article, in which
Eq.(4) is interesting...
http://physics.trak4.com/GR_Charge_Couple.pdf
I'll post here,

S^2 = X^2 + ab , Eq.(4) .

That is an electrical expression of the Einstein
Field Equations "Guv=Tuv".

That same equation(4) can be generated by pure
logic...

By generating successive dimensions, beginning
with "0" produces,

$ 0 dX = e , $ e dX = eX , $ eX dX = eX^2 /2...

unit length "e" followed by indefinite area "eX", etc.

The unit length "e" is perpendicular to all successive
dimensions, thus scalar product e.X= 0, as the use
of integration developes more dimensions with "e"
being the "fundamental unit length".

Set up a Pythagorean vector distance S = X + e,
and then relate two points "a" and "b" that have a
magnitude +/- |e| parallel to "e" to enable,

S(a) = X+a , S(b) = X+b .

X is the orthogonal distance between "a" and "b".

At that point, the scalar product S(a).S(b) yields

S^2 = X^2 + ab,

to reproduce Eq.(4), and the electrical EFE's.

The EFE's can be processed electrically provided
the relation to generic mass is defined, and it is.
We have the electric and gravitation effects explained
but I'm uncertain as to how the invariant "c" can be
derived.

[Ken S. Tucker]

Hi Charles.
On Aug 25, 5:50 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
...
> There is another problem with the notion of cause preceding effect. This
> is a view which we impose on the world as a result of our experience of
> the macroscopic behaviour of matter, resulting from the law of entropy.
> The laws of physics, otoh, are time symmetrical. I do not consider that
> we can justify this constraint at a fundamental level, and nor do I even
> see how to describe it in a quantum context.

Perhaps we need to understand Action (h), Energy (E=h/t)
and Power (E/t=h/t^2). There seems to be a tendency to
focus on Energy and it's conservation.
Is Action conserved? Is Power conserved?

Let's consider Action. System S1 passes an action h
to system S2,

S1-h ---->h----> h+S2

using any of the 4 known conventional forces, we
term, gravity, EM, weak and strong. The Action h
is held to be a constant and invariant, apart from
the nature of the causal force.

The concept of Action also has angular momentum
(spin) and also the product of two charges "a" and "b",
each is fundamental.

Where the so-called "arrow of time" is concerned,
Power has a t^2 so it makes NO diff if "t" is +/- , to
give us a lead. A problem still exists (for me) that
the charge product can + or - that is h = +/- |h|,
but that renders the concepts of "repulsion" and
"attraction".

We theoreticians seem bound by rules that respect
the indivisability of "h", so an ordinary derivative
CANNOT be employed to "h", there is no such
thing as "dh", empirically, (that I ever read).

Let's use "D" as a finite increment and study an
implication, such as, E = h/t == Dh/Dt.
That Dh/Dt cannot be taken to the limit dh/dt, so
that means we need a new calculus.
Regards
Ken S. Tucker

[Ken S. Tucker]

On Aug 25, 12:39 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>

>
>
>
> >Hi Charles.
> >On Aug 25, 5:50 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> > ...
> >> There is another problem with the notion of cause preceding effect. This
> >> is a view which we impose on the world as a result of our experience of
> >> the macroscopic behaviour of matter, resulting from the law of entropy.
> >> The laws of physics, otoh, are time symmetrical. I do not consider that
> >> we can justify this constraint at a fundamental level, and nor do I even
> >> see how to describe it in a quantum context.
>
> >Perhaps we need to understand Action (h), Energy (E=h/t)
> >and Power (E/t=h/t^2). There seems to be a tendency to
> >focus on Energy and it's conservation.
> >Is Action conserved? Is Power conserved?
>
> >Let's consider Action. System S1 passes an action h
> >to system S2,
>
> >S1-h ---->h----> h+S2
>
> >using any of the 4 known conventional forces, we
> >term, gravity, EM, weak and strong. The Action h
> >is held to be a constant and invariant, apart from
> >the nature of the causal force.
>
> >The concept of Action also has angular momentum
> >(spin) and also the product of two charges "a" and "b",
> >each is fundamental.
>

> In my view, action is no more than a mathematical trick. It is not
> fundamental.

I think, prior to conclusions, we might consider
Weinbergs "Grav&Cosmo", chp 12, "THE ACTION
PRINCIPLE", since he worked hard to write it.
Eq.(12.3.2), begins an interest followed by,
"*Thus the energy-momentum tensor... if and only
if the matter action is a scalar*".

Ok, I can produce improvements, on his approach,
but "mathematical trick" is disagreeable.

> >Where the so-called "arrow of time" is concerned,
> >Power has a t^2 so it makes NO diff if "t" is +/- , to
> >give us a lead. A problem still exists (for me) that
> >the charge product can + or - that is h = +/- |h|,
> >but that renders the concepts of "repulsion" and
> >"attraction".
>
> >We theoreticians seem bound by rules that respect
> >the indivisability of "h", so an ordinary derivative
> >CANNOT be employed to "h", there is no such
> >thing as "dh", empirically, (that I ever read).
>

> Actually there is such a concept. The principle of least action makes
> dh=0. We only have empirical law when action is minimised.

Thanks for the correction.

[Ken S. Tucker]

ACTION

Hello all.
I removed this from the "Causality" thread.

On Aug 25, 12:39 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>

...

> >Let's consider Action. System S1 passes an action h
> >to system S2,

> >S1-h ---->h----> h+S2

> >using any of the 4 known conventional forces, we
> >term, gravity, EM, weak and strong. The Action h
> >is held to be a constant and invariant, apart from
> >the nature of the causal force.

> >The concept of Action also has angular momentum
> >(spin) and also the product of two charges "a" and "b",
> >each is fundamental.

Charles writes,

> In my view, action is no more than a mathematical trick. It is not
> fundamental.

((Tucker grabbed his chest and swallowed a
1/2 bottle of glycerine capsules, I'm ok now))

Let Action = Energy*Time.
(h=6.625*10^-27 ergs*seconds).

Tucker does carpentry and is the boss, and
watches Alice hammer in 100 nails/hour and
Bob 200 nails/ hour.
They both use the same hammer strike.
Bob strikes twice as fast as Alice, thus
has twice the frequency, I can hear.

I pay for energy, such as Kilowatt*hours,
(Power*Time) in electricity.
Each nail hammered in takes a fixed
amount of energy.

Bob expends twice the energy that Alice
does per hour.
Energy(Bob) = 200 Actions/hour
Energy(Alice) = 100 Actions/hour

I pay Bob $200/hour and Alice $100/hour.

Next: another Guy' is flying by at 8/10 c,
where gamma=1/sqrt(1-v^2/c^2) = 10/6.

To Guy' the Energy' = Energy*10/6 of what
Tucker measures because of Guy's kinetic
energy, and Guy' sees Tuckers clock run
slower by an amount, Time' = Time*6/10.

Guy and Tucker agree that,

Action = Energy' * Time' = Energy * Time

and then Tucker and Guy agree that $1/action
is the relativistic rate of payment.
======================

I think, prior to conclusions, we might consider
Weinbergs "Grav&Cosmo", chp 12, "THE ACTION
PRINCIPLE", since he worked hard to write it.
Eq.(12.3.2), begins an interest followed by,
"*Thus the energy-momentum tensor... if and only
if the matter action is a scalar*".

===========================

[Eric Gisse]

On Aug 26, 2:05 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
[snip]

Get a blog, Ken. The solid month of you talking to yourself makes you
look even more insane than you already seem.

[Ken S. Tucker]

Hi Juan

On Aug 26, 4:40 am, "Juan R." González-Álvarez
<juanREM...@canonicalscience.com> wrote:
> Ken S. Tucker wrote on Sun, 24 Aug 2008 13:29:16 -0600:
...
> > Can you provide an independent ref to those " GR theorems" ?.
> > Regards
> > Ken S. Tucker
> > [...]
>
> Robert J Low, "Speed Limits in General Relativity," Class. Quant.
> Grav. 16 (1999) 543,http://arxiv.org/abs/gr-qc/9812067.
>
> is the paper cited by Carlip as 'proof' that interactions in gravity are
> retarded. This has no experimental basis and theoretically it lacks
> considering the g_ab(R(t)) components, which are not taken into account
> in general relativity.

I was quite surprised by the latitude of solutions
the GR EFE's permit. An analysis of an electrical
configuration of two charges finds the EFE gives
a metric (see Eq.2) here,
http://physics.trak4.com/GR_Charge_Couple.pdf
that is defined by a *length* from "a" to "b", and
most importantly, the solution works!

I suggest you put your metric into the EFE's and
see what you get, I'd be curious to know.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Chalky

On Aug 28, 4:25 am, Chalky <chalkys...@bleachboys.co.uk> wrote:
> On Aug 27, 7:28 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > For me it is quite interesting to see that I pay for
> > action (not energy) in my electric bill,
>
> If that were true, your bills would be 9 times as high if you paid
> quarterly than if you paid monthly.
> In practice you pay for the total energy consumed in an agreed time
> period (time typically measured as a proportion of a revolution of the
> Earth round the Sun), not the total energy consumed multiplied by that
> time period.
>
> > both Action and money being invariant.
>
> Money is so NOT invariant that it buys substantially less energy now
> than it did 6 months ago and I didn't even need to move to discover
> that).

The money is invariant, what you can buy with it
is shrinking :-).

> However, despite your garbled analogy in places,

Thanks, I'll try to improve on my garbling.

> you have succeeded in
> convincing me that action is Lorentz invariant (as is any given number
> of nails)

Good, (ok $1/nail).

> What I find potentially interesting is why this would be (for action).
> The boring answer would be that the relativistic energy transform is
> the inverse of the relativistic time transform.

Agreed, I find GR is easier to understand using the
invariance of action.

> A more potentially
> intriguing explanation might be that, with units of force x distance x
> time, it provides a more intimate fusion of the concepts of energy
> (force x distance) and momentum (force x time) , than the energy-
> momentum 4 vector achieves?

I suggest NOT using force in GR, the force vanishes
by definition, even Lorentz Force.
I've been following the thread on 4 momentum.
Here's a paragraph on the subject,
http://physics.trak4.com/MST_PlancksConstant.pdf
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Charles and Chalky.

On Aug 29, 7:29 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Chalky <chalkys...@bleachboys.co.uk>

>
> >> I suggest NOT using force in GR, the force vanishes
> >> by definition, even Lorentz Force.
>

> >If something I experience and use fruitfully every day vanishes within
> >the context of a particular theoretical model, I am inclined to
> >conclude that this represents a weakness of the theoretical model, not
> >a weakness in my own experiences, actions and observations.

It's a matter of understanding the meaning of
Lorentz force mathematically (#). While you are
sitting on your chair, can you regard yourself
as being at rest?

> May I just clarify that the Lorentz force does not vanish in GR. Only
> the gravitational force vanish in a local inertial reference frames.

Charles, Lorentz force does vanish in GR.(#)
Acceleration is relative in GR, as uniform motion
is relative in SR.
See the dichotomy, if all uniform motion is relative
then how does a change in uniform motion create
an absolute acceleration? So you now circulate
back to absolute uniform motion if the Lorentz
force is an absolute force and acceleration.

(#) This thread has a more complete explanation,
"Vanishing of Lorentz Force?" , Feb,12 2008.

Perhaps we should consider the equation
U^u;w U^w =0 ,
where U^u and U^w are 4 velocities ?
I think it's vital to RQG.

[Ken S. Tucker]

Hi Charles

On Aug 30, 6:20 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
> >> "absolute" or, rather *proper* acceleration is the acceleration away
> >> from inertial motion. Do not confuse inertial motion (meaning no active
> >> forces) with uniform motion, which is relative.
>
> >So are you suggesting that "absolute" acceleration exists in GR?
>
> I do not like that terminology, but iirc you pointed out that Weinberg
> uses "absolute acceleration" to mean the derivative of 4-velocity with
> respect to proper time.

Yes in Grav& Cosmo, DU^u/Ds = f^u/m , Eq.(5.1.11).

However note you can consider your motion as zero
relatively to yourself so that DU^u/Ds=0 for any FoR.
Most importantly, the Laws of Physics must be true
in your FoR.

> I would prefer to call it "proper acceleration".
> This quantity is a 4-vector and, multiplied by (scalar) mass, gives the
> Force 4-vector, as used in the Lorentz force law
>
> (Force)^i = F^ij J_j
>
> This is a covariant equation, holding in all coordinate systems
> (inertial or not).

True, however see GR1916 Eq.(65a) and onward,
and find that to vanish in GR, (This link might work)...
http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200...
((Simple Simon posted one that does)) I covered that in
the thread "Vanishing of Lorentz Force?" Feb 12, 2008.

You may interested to find that AE's GR1916 Eq.(66)
requires the Lorentz force to vanish as does Weinberg's
equivalent Eq.(5.3.7).

> http://www.teleconnection.info/rqg/IntroductionToTensors#Electromagnetic
> Force

Does your treatment prevent an electron from spiralling
into the nucleus?
We find f_u =0 will create a "quantum geodesic" to
prevent the classically predicted spiralling, and that is
posted here, "Vanishing of Lorentz Force?" Feb 12, 2008.

[Ken S. Tucker]

Hi Charles.
At the outset, let me explain I explore many different
ways to solve a problem.

On Aug 30, 11:15 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>

> >Hi Charles
> >On Aug 30, 6:20 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
> >> >> "absolute" or, rather *proper* acceleration is the acceleration away
> >> >> from inertial motion. Do not confuse inertial motion (meaning no active
> >> >> forces) with uniform motion, which is relative.
>
> >> >So are you suggesting that "absolute" acceleration exists in GR?
>
> >> I do not like that terminology, but iirc you pointed out that Weinberg
> >> uses "absolute acceleration" to mean the derivative of 4-velocity with
> >> respect to proper time.
>
> >Yes in Grav& Cosmo, DU^u/Ds = f^u/m , Eq.(5.1.11).
>
> >However note you can consider your motion as zero
> >relatively to yourself so that DU^u/Ds=0 for any FoR.
>

> No. This is not true. You only have DU^u/Ds=0 if you are in inertial
> motion.

Hmm, if you have a "proper change" in your acceleration
given by DU^u/Ds as you allude to, and a fella on the other
side of the Earth (Australia) claims the same, why are
you both at relative rest?

> >Most importantly, the Laws of Physics must be true
> >in your FoR.
>
> >> I would prefer to call it "proper acceleration".
> >> This quantity is a 4-vector and, multiplied by (scalar) mass, gives the
> >> Force 4-vector, as used in the Lorentz force law
>
> >> (Force)^i = F^ij J_j
>
> >> This is a covariant equation, holding in all coordinate systems
> >> (inertial or not).
>
> >True, however see GR1916 Eq.(65a) and onward,
> >and find that to vanish in GR, (This link might work)...
> >http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200...
>

> http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf

Thanks buddy.

> >You may interested to find that AE's GR1916 Eq.(66)
> >requires the Lorentz force to vanish as does Weinberg's
> >equivalent Eq.(5.3.7).
>

> That isn't true. The vanishing of the Lorentz force is required for
> inertial motion, not in general.

Charles, I've cross referenced to two Nobel Prize
winners, provided their Eqs, and explained the
meaning of those equations using analogies and
mathematics. I/we went further to check the impact
of those equations on electron orbitals, and found
empirical agreement, so I think the study is worthy.

> >>http://www.teleconnection.info/rqg/IntroductionToTensors#Electromagnetic
> >> Force
>
> >Does your treatment prevent an electron from spiralling
> >into the nucleus?
>

> For that one must deal with qed, not the classical Lorentz force.

Charles, you imply classical Lorentz force does not
apply to that problem...(what ever classical means).
However the GR application (f_u=0) of the Lorentz
force does indeed prevent the "classical" idea of
electrons from spiralling into the nucleus without
needing qed.
That is good empirical evidence for f_u=0, and as I've
showed at this link,
http://groups.google.com/group/sci.physics.foundations/browse_thread/thread/a3453bd8b85313a4/2c63bc0e5d42d357?hl=en&lnk=gst&q=Vanishing+of+Lorentz+Force%3F#2c63bc0e5d42d357
(Vanishing of Lorentz Force?)
is entirely in accord with EM and moreover EMR,
so I'm keeping an open mind.

[Ken S. Tucker]

Hello Dr. Enders et al.

On Aug 30, 2:35 am, Peter <end...@dekasges.de> wrote:
> > >> > Charles writes,
> > >> > In my view, action is no more than a mathematical trick. It is not
> > >> > fundamental.

> > "Cl\.Massé" <a...@c.com> writes:
> > In the derivation of the Schrödinger equation from the Hamilton-Jacobi
> > equation, S becomes the phase of the wave.
>
> In the 2nd footnote of the 2nd Communication 1926, S. expressis verbis
> refrains from this result of his 1st Communication
>
> > It is especially clear for
>
> monochromatic
>
> > light, were S is the time taken from a point to another, and then the phase
> > difference between those points since its speed is constant. In first
> > quantization, the least action principle is equivalent to the Fermat
> > theorem,
>
> which is the role of "first quantization" here?
>
> > that gives the points of constructive interference, where the phase
> > is stationary as a function of the path.
>
> is constructive interference tied to stationarity of phase?
>
> > Feynman's paths integrals are but a rehashing of those ideas.
> > It is even interesting to note that the least action fulfills all the
> > properties of a distance. That's why Einstein used it to define the
> > geometry of space-time, through light rays. That is surely useful for
> > those who are investigating theories without prior space-time.
>
> I think so, too

I also agree.

> Let's recall Leibniz's formula
>
> action = mass x path length x velocity
>
> When velocity=const (light), action ~ path length, but what, if not?

I find, mass=energy/c^2 , "path length" = 1 wavelength = L,
energy= h*f , f*L = c , (f=frequency) then,

action = (hf/c^2)Lc = hfL/c = h which looks good.

but the so-called "path-length" uses L.

Fred & Andy (IIRC) developed a photon theory that required
2L, (2 cycles) which is advanced.

I find an exact relation between the classical cycle
and the action "h" is still debateable, but I lean to
Fred and Andy's model.

> > I would say, action more fundamental than anything else, and still more so
> > in gauge theories.
>
> I'm wondering about the intimate relationship between Lagrangian, L, and
> symmetry, where L itself has no immediate physical meaning (Helmholtz called
> L the 'kinetic potential', but this applies not generally), do you know an
> explanation of that?

I'll try. A ball bouncing inelastically on a hard
surface repeats its trajectory cyclically with
a constant Lagrangian. If that ball where to hit
a place on the surface that is soft, that surface
would heat up and the ball would loose kinetic
energy at that bounce. Hence the Lagrangian
puts heat (kinetic energy) in that soft surface
and the Lagrange reduces.

> Thank you,
> Peter

Best again to you.
Ken S. Tucker

[Ken S. Tucker]

Hi Harald and all.

On Sep 3, 3:18 am, "harry" <harald.vanlintelButNotT...@epfl.ch> wrote:
> Ken S. Tucker wrote:
> > On Sep 1, 7:10 am, "harry" <harald.vanlintelButNotT...@epfl.ch> wrote:
> >> "Ken S. Tucker" <dynam...@vianet.on.ca> wrote in
> >> messagenews:8d81cf0c-4787-4311...@l33g2000pri.googlegroups.com...

>
> >>> Hi Charles
> >>> On Aug 30, 6:20 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >>>> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>

> >>>>> If a particle (or a charge) has zero acceleration is there
> >>>>> a force on that particle?
>
> >>>> This is a different definition of force, using Newton's second law
> >>>> and applied to force treated as a 3-vector. We can choose a
> >>>> non-inertial frame in which the impressed force balances the
> >>>> inertial force (as we do when we consider our own local frame, in
> >>>> which gravity balance the force exerted by the chair we are
> >>>> sitting on), but usually we describe this as a state of
> >>>> equilibrium between forces, not a state in which there are no
> >>>> forces.
>
> >>> Agreeable for Newton, although imv GR treats
> >>> that sitting on a chair, using the stress energy
> >>> tensor, where the detail is in how the cushion
> >>> is deformed, it's like storing energy in a spring,
> >>> that will increase it's g-field via E=mc^2.
>
> >> That deformation corresponds to Hooke's force law. This is an
> >> obvious case of force equilibrium.
>
> > True in Newtonian thinking, however we are in GR,
> > using the stress tensor.
>
> I'm not "in GR", in the sense that I don't share the orginal philosophy
> behind it.

I didn't know that Harald, sometime when you get a
chance I like to read more about that.

> Nevertheless, when talking about "force equilibrium" one does not
> refer to "stress tensors" but to forces, and Hooke's force law is applied in
> the 21 century in nearly every scale.

Not necessarily, force cannot be directly measured,
it is an extrapolation from a change in stress such as,
http://en.wikipedia.org/wiki/Piezoelectricity

Consider getting on a bathroom scale, the meter spins
to output the change in force. If I *cheat* I can change
the meter to read less, all the way to zero. Therefore
I have done a transformation to a CS wherein the force
vanishes.
Now when I step off the scale, I get a change in force
per change in time, and the scale reads negative.

You can pich up how Hooke's Law relates to GR here,
http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor

> > Newtons ideas compared to GR is like comparing
> > the game of Checkers to Chess, a different set of
> > rules and thinking.
>
> Yes indeed!

When we stepped onto the scale, we changed the stress
in a quantized way, either by generating electricity, or by
compressing (and thus heating) a spring. What GR can
do is explain that quantized output.

> Regards,
> Harald

Same to you Harald.

[Ken S. Tucker]

Hi Peter.

On Sep 3, 2:24 pm, Peter <end...@dekasges.de> wrote:
> > You can pich up how Hooke's Law relates to GR here,
> >http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor
>

> I have not found Hooke's law there, please help

Yes, here's Hooke's "Law" in this ref,
http://en.wikipedia.org/wiki/Piezoelectricity#Mathematical_description

> J.E is not the mechanical energy density, u_mech, as stated there.

J.E =0 , always, so there is no such thing as J.E,
however that equation is important as a constraint,
since it always vanishes. IOW's if it doesn't vanish
we're in trouble, because J.E=0 is proven empirically
and forms the basis of QT.

From the standpoint of a technician (like myself)
who needs to understand current flow, I'll rewrite
J.E as,

J./\E = (J=qV) . (/\E + /\E') = 0

and solve to,

qV./\E = - qV./\E' .

which are in Power units.

In the case of a conducting wire the current "qV" is
constant, but there is a *quantized* power loss
" -qV./\E " via heating the extension cord to the
electric lawn mower.
Electricians call that a voltage drop through the
conductor due to resistance.
Regards
Ken S. Tucker
PS: Did I just demo GR and QT using a lawn mower
and extension cord ???

[Ken S. Tucker]

On Sep 4, 2:55 am, "harry" <harald.vanlintelButNotT...@epfl.ch> wrote:
> "Ken S. Tucker" <dynam...@vianet.on.ca> wrote in messagenews:6eb92307-8207-4e10...@r15g2000prh.googlegroups.com...

> That chance pops up immediately here below. :-)

>
> >> Nevertheless, when talking about "force equilibrium" one does not
> >> refer to "stress tensors" but to forces, and Hooke's force law is applied
> >> in
> >> the 21 century in nearly every scale.
>
> > Not necessarily, force cannot be directly measured,
> > it is an extrapolation from a change in stress such as,
> >http://en.wikipedia.org/wiki/Piezoelectricity
>

> It depends on what you mean with "directly measured". But we may take
> Hooke's law as a definition of force. :-)

Not really, it's 3D, see
http://en.wikipedia.org/wiki/Hooke's_law

> > Consider getting on a bathroom scale, the meter spins
> > to output the change in force. If I *cheat* I can change
> > the meter to read less, all the way to zero. Therefore
> > I have done a transformation to a CS wherein the force
> > vanishes.
>

> That "vanishing" *is* cheating: the spring is not in equilibrium, and that
> can even be easily verified. In other words, that force vanishing is a
> simple example of hiding what is physically truly there.

How do you find that physical truth?
(I think you'll need to use the force to output
energy/time = Power for measurement)

> Note: that happens to be exactly what makes me disagree with the original GR
> philosophy, according to which gravitational fields can be made to "really
> vanish" so that a body's gravitational field "does not exist", eventhough in
> fact it's only apparently so.

That slides from the PoE to Tidal effects.

> > Now when I step off the scale, I get a change in force
> > per change in time, and the scale reads negative.
>

> > You can pich up how Hooke's Law relates to GR here,
> >http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor
>

> I will quickly admit that there is a connection. :-)

>
> >> > Newtons ideas compared to GR is like comparing
> >> > the game of Checkers to Chess, a different set of
> >> > rules and thinking.
>
> >> Yes indeed!
>
> > When we stepped onto the scale, we changed the stress
> > in a quantized way, either by generating electricity, or by
> > compressing (and thus heating) a spring. What GR can
> > do is explain that quantized output.
>

> The word "quantized" confused me for a second. :-)
> Of course GR can explain that output, but I don't think that GR does a
> better job at that than classical (pre-GR) mechanics.

I can demo my understanding using vanilla light
tensors with a helping of physics on the side.
GR puts many concepts in the same pot.

An "energy density" (aka stress tensor) , T^uv has
a Divergence (T^uv;v=0) of zero, meaning energy
in = energy out of a small (infinitesmal) volume,
to stand for the Conservation of Energy and as a
sideline, force f^u = T^uv;v =0.

OTOH, T^uv is NOT constant, it can be changed
*incrementally* "/\", by (T^uv + /\T^uv);v =0.
where /\T^uv is an incremental change in the
energy density, IOW's, a finite change /\T^uv,
where /\T^uv;v=0.

It's at that point we become mathematically
illiterate, as we accept an incrementally change
"/\T^uv" but NOT a continous variation of that
incremental change which is /\T^uv;v = 0.

> Cheers,
> Harald

Cheers back :-)
Ken S. Tucker

[Ken S. Tucker]

> Not really, it's 3D, seehttp://en.wikipedia.org/wiki/Hooke's_law

Suppose we have a photon coincident with a
point, figuratively,

point
~~~~~O~~~~~>

At point "O", the photon is either a {1,0}, ie. it's there
or NOT there.
We can represent that by the Kronecker delta,
that has a *covariant* derivative of zero, however
/\T^uv =/=0, when the photon is coincident with the
point "O", because the photon *instanteously* changes
the energy density at that point "O" and then changes
back to zero, instanteously.
I think that is describing: what is the derivative of
a digital variation?
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Charles And Peter.

On Sep 5, 12:19 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>

> >Hi Peter.
>
> >On Sep 4, 4:00 pm, Peter <end...@dekasges.de> wrote:
> >> > >> Oh No <N...@charlesfrancis.wanadoo.co.uk> writes:
> >> > >> > Thus spake Peter <end...@dekasges.de>
> > ...
>
> >Peter
> >> > >Let me add the following thought about your radar method.
> >> > >If you have a time delay during reflection, you obtain the Schwartzschild
> >> > >metrik, have I understood this correctly?
>
> >Charles
> >> > Correct (for an idealised particle in isolation)
>
> >> > >The Schwartzschild metrik is not
> >> > >Lorentz covariant (or invariant), correct?
>
> >> > Incorrect. The metric is a tensor, so of course it obeys covariance (not
> >> > invariance)
>
> >Peter
> >> if so, my idea - that any non-constant g_mn is not compatible with Lorentz's
> >> transformation - breaks down
>
> >A glance at the LT shows it applies to a constant velocity,
> >giving (ct)^2 = r^2, for light speed and ds^2 = (cdt)^2 - dr^2,
> >for any speed.
>
> It applies to any vectors

Yes, I stand corrected. I should have wrote, the LT is
a transformation relating two CS's moving with constant
velocity, as in this,
http://en.wikipedia.org/wiki/Lorentz_transformation
It's simply SR.

> >When the g_mn are "not constant", such as in GR, then
>
> >ds^2 = g_mn dx^m dx^n ,
>
> >is pretty much the GR LT equivalent, and applies to
> >acceleration such as in the Schwartzchild metric.
> >There are legalese strings attached, but that's the
> >upshot.
>
> The non-constancy of the metric is not relevant.

I was trying to avoid "legalese" :-).

> At any point the manifold is locally Minkowski.
> Vectors are defined at a point.

Well the LT applies to spacetime where the Riemann
Christoffel Curvature tensor (R_abcd) is zero, such
that Peter's g_mn can be *transformed* to constants,
I think that's was his intent, it is clear to me.

>(Note: there is no such thing as a displacement vector in curved spacetime).

Well of course there is, otherwise our common concept
of "radar ranging" in a g-field would be meaningless.
Maybe that deserves a separate thread though.

[Ken S. Tucker]

On Sep 5, 11:08 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
> On Sep 4, 11:50 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
> > On Sep 4, 2:55 am, "harry" <harald.vanlintelButNotT...@epfl.ch> wrote:

...

> ======================================= MODERATOR'S COMMENT:
> /\T^uv;v is not an "incremental change"; your photon represents an infinite energy density - this and other flaws let me reject this posting

Hi Mr. Moderator.
This is why I dislike using tensor analysis in SPF unless
Jay Yablon is available, because it's unpopular, though I
can see my "style" can be improved.
You can pick up the T^uv;v = 0 here,
http://en.wikipedia.org/wiki/Stress-energy_tensor#In_general_relativity

I can improve my delivery using (T^uv);v =0.
Then with a finite increment " /\T^uv " inserted in the
brackets, we form,

(T^uv + /\T^uv);v = 0 = (T^uv);v + (/\T^uv);v .

It follows that (/\T^uv);v = 0, although (/\T^uv) =/=0.
Is that better?
If that's ok, (and this gets posted) I'll try to address
the issue of "infinite energy density" you mentioned.
Regards
Ken S. Tucker

[Ken S. Tucker]

To whom it may concern.

> You can pick up the T^uv;v = 0 here,http://en.wikipedia.org/wiki/Stress-energy_tensor#In_general_relativity

>
> I can improve my delivery using (T^uv);v =0.
> Then with a finite increment " /\T^uv " inserted in the
> brackets, we form,
>
> (T^uv + /\T^uv);v = 0 = (T^uv);v + (/\T^uv);v .
>
> It follows that (/\T^uv);v = 0, although (/\T^uv) =/=0.
> Is that better?
> If that's ok, (and this gets posted) I'll try to address
> the issue of "infinite energy density" you mentioned.
> Regards
> Ken S. Tucker

Awhile ago, in this group, we discussed the derivative
of a photon, that is being theoretically interogated in
this posting history.
A photon coincident with some point "O" in the Fig
above, creates (I presume) a digital 0,1,0 at "O", that
we call a square pulse, again, it's a case of whether
the photon is there or not there. Now certainly, when
I shine a laser across the room photons will pass a
point "O", though the resolution is finite, not a point.

There is some animation here that's very pretty,
http://en.wikipedia.org/wiki/Square_wave
and shows the Fourier series developement.

Imv, that Fourier enables the *differentiation* of a
digital pulse, and also a calculation of the probablity
of it's location, they seem to be two words that mean
the same thing.
So the term I used above, " /\T^uv " could be expressed
as a digital conversion to a continuum, and in so doing,
unites GR and QT fundamentally, provided (/\T^uv);v =0,
in the aforementioned differentiation, so Conservation
of Energy holds.
Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Charles, it's Sunday so I suppose pseudo
religious concepts are acceptable...

On Sep 7, 6:07 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> I am on the final section of the website, in which I compare the
> predictions of relational quantum gravity with observation and with
> those of standard cosmology. I have posted the results of the supernova
> analysis, with graphs, and comparison of the properties of the models

IMHO...
There is no such thing as "standard cosmology".
The Big Bang is conjecture, based on the desire
of humans to assign a mortality to the universe
in *mans own image* like orgasm to death, that's
the same thinking the pope used to screw Galileo
and scare Copernicus, by maintaining a universe
that can be sold to the un-washed masses via
selling cheap paperbacks.

OTOH, I/we regard an *immortal* universe as
"standard cosmology". If this ref is ok,
http://en.wikipedia.org/wiki/Solar_wind#Emission
we have a measurement (using real science) of
6.7 billions tons/hour of e- and p+ particles blown
off the Sun, that is transparent. Indeed the clarity
of Hubble galactic images shows no distortion,
(apart from red-shift).
That dismisses the idea that e- or p+ can absorb
photons, except when operating as a dipole, such
as in an H atom, otherwise we would have evidence.

Where the "red-shift" is concerned, see Golowich's
et al 1989 paper, "Gravitational scattering of quantum
particles", that predicts a red-shift through a transparent
gas.

Where the "dark matter" is concerned the e- and p+
particles blown off stars eventually combine to form H,
and in so doing emit radiation.

The so-called "dark matter" consists of e- and p+
that can be 100's of time more massive than all the
stars combined because of the time it takes for those
particles to reform a star.

The above model rely's on *known* physics, based
on scientific measurements.

[Ken S. Tucker]

Hi Kwan and friends.
I'll snip and ref to Kwan's original post.
((In SPF))

Kwan's Eq. set(2.5) such as W1= &J2/&J3 - &J3/&2
*looks* like "inertial coupling" in aerodynamics,
http://en.wikipedia.org/wiki/Flight_dynamics
using pitch, yaw, roll.
What would be the invariant "W" ?
Of course one has derivatives and 2nd derivatives
(accelerations) when flying airplanes.

Your Eq.(6.1) is fascinating, however a generalization
of the vector product is doable using the "permutation
tensor" ...
http://en.wikipedia.org/wiki/Levi-Civita_symbol
in place of terms like "plane angle rotations" and
"solid angle rotations". Our mathematician friends
have developed thoses concepts to "n" dimensions,
e(a,b) = -e(b,a) , e(a,b,c)...etc.
That might save you alot of explanation time.

Who knows, maybe a better notation might be,
F(2) = e(a,b) , F(3) = e(a,b,c) and so forth to evolve
the 4 known forces as your rotations become more
complex.

John Baez has a blog, and he is studying catagory
theory, so you may want to post to his blog too.
I think he would be interested in your PoV.
Cheers
Ken S. Tucker

[Ken S. Tucker]

Hi Charles, it was Sunday so I suppose pseudo
religious concepts are acceptable...

On Sep 7, 6:07 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:

> I am on the final section of the website, in which I compare the
> predictions of relational quantum gravity with observation and with
> those of standard cosmology. I have posted the results of the supernova
> analysis, with graphs, and comparison of the properties of the models

IMHO...
There is no such thing as "standard cosmology".
The Big Bang is conjecture, based on the desire
of humans to assign a mortality to the universe
in *mans own image* like orgasm to death, that's
the same thinking the pope used to screw Galileo
and scare Copernicus, by maintaining a universe
that can be sold to the un-washed masses via
selling cheap paperbacks.

Fred, I think you'll be interested in this part.

[Ken S. Tucker]

On Sep 10, 1:35 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>

> >Hi Charles, it was Sunday so I suppose pseudo
> >religious concepts are acceptable...
>

> not really, but...

It has to do with theoretics. It's the Scientific method
(using reproducible experiments) vs. Theoretical notions,
such as Black Holes, Big Bangs upon which the BH-BB
cosmology is based, that obviously requires a leap of faith.

> >On Sep 7, 6:07 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> >> I am on the final section of the website, in which I compare the
> >> predictions of relational quantum gravity with observation and with
> >> those of standard cosmology. I have posted the results of the supernova
> >> analysis, with graphs, and comparison of the properties of the models
>
> >IMHO...
> >There is no such thing as "standard cosmology".
>

> That is not something to have an HO about. The standard cosmology is the
> one widely accepted as such.

I studied this article,
http://www.teleconnection.info/rqg/Supernova
Therein you have suggested an older universe,
as an improved cosmology. What I do is go a
bit further to -oo and eliminate BH's and BB's,
and retain Conservation of Energy.

> >The Big Bang is conjecture,
>

> No, it is logical deduction from almost undeniable postulates. Perhaps
> it can be replaced in a theory of quantum gravity with a big bounce (as
> in LQG) but in general terms there is almost no scientific room for
> manoevre.

An immortal universe fits the data better.

> >Where the "red-shift" is concerned, see Golowich's
> >et al 1989 paper, "Gravitational scattering of quantum
> >particles", that predicts a red-shift through a transparent
> >gas.
>

> I have seen such papers. They do not reproduce observation, and leave
> much else unaccounted.

They work for us, in excellent agreement with reality.

> >Where the "dark matter" is concerned the e- and p+
> >particles blown off stars eventually combine to form H,
> >and in so doing emit radiation.
> >The so-called "dark matter" consists of e- and p+
> >that can be 100's of time more massive than all the
> >stars combined because of the time it takes for those
> >particles to reform a star.
>

> Such theories also do not fit the numbers.

Again, they work for us, the co-efficients adjust.

> >The above model rely's on *known* physics, based
> >on scientific measurements.
>

> Untrue.

It's true because we don't need to break known Physical
Laws nor introduce any new hypothesis, we use what is
known and tested.

[Ken S. Tucker]

Hi Jim.

On Sep 12, 7:03 am, JimJast <jim_jastrzeb...@yahoo.com> wrote:

> On 12 Wrz, 04:35, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > > >The above model rely's on *known* physics, based
> > > >on scientific measurements.
>
> > > Untrue.
>
> > It's true because we don't need to break known Physical
> > Laws nor introduce any new hypothesis, we use what is
> > known and tested.
>

> Hi Ken,
>
> Who needs known Physical Laws?
> Only engineers can make money on them, surely neither physicists nor
> mathematicians who already have figued out that if energy were
> conserved the Big Bang Hypothesis couldnt be true, what I had been
> telling them since February 1985, when I calculated Hubble constant
> just from the principle of conseration of energy and Einstein's
> relativity, and got the value seen in the sky.

Yes, that's the way I compute it too.
Simply, it's a case of shooting a particle threw a rarified
gas at absolute zero temperature (0K), where no contact
forces (apart from gravitational interaction) occur.
The particle gravitationally pulls on the gas to produce
relative accelerations in the gas, and thus kinetic energy,
because relative motion in the gas is produced and the
temperature is then greater than 0K when the particle
exits that region.
Of course the CoE requires the particle surrenders some
kinetic energy to heat the gas. Relativity enables photons
to gravitationally interact with the gas, however photons
changing in energy appears as a "red-shift" in place of a
velocity change.
Is that what you get?

It's bit more complicated, I subbed in universal density
into the "cosmological constant" and found a good fit.

> So finaly they agreed
> and cancelled the principle of conservation of energy (which is
> actually only a half what I wanted to achieve).
> Now we are going to see a renaissance of perpetual motion machine
> inventions. Physics students in my university started already betting
> with me that they'll show me how energy can be created (they already
> believe their professors that energy is not conserved "in general
> relativity" and so it may be created since the universe is obviously
> relativistic (as I keep telling them), They don't know yet how to
> create energy, but being smart young fellows they are going to figure
> it out soon. And if one thinks about it, if energy couldn't be created
> how the whole universe could. Right? A phrase "let it be" said by some
> god at right time might be enough (as some of those professors
> believe). Why not? Surely you can't prove that it is a wrong
> hypothesis. Due to the Laws of Epistemology you may only believe it is
> not a right one. As I don't believe in the BB hypothesis but everyone
> in our Cosmology and Gravitation dept. tells me that I'm the only guy
> in the whole wide world who does not agree, so I must be wrong, even
> if Laws of Math agree with me.

Well Jim, tell them you found some hermits living in
the woods that agree with you. I also read a bit about
you and you have an ally where nonsymmetrical metrics
are concerned.

> -- Jim

Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Dr. Enders and all.
On Sep 11, 2:46 pm, Peter <end...@dekasges.de> wrote:
...
> All Lagrangians I know are of dimension energy (it's not a matter of units,
> but of dimension), and this is necessary for reproducing the Newtonian
> equation of motion and for connecting to a Hamiltonian which can represent
> the total energy of a system

If anyone has Weinberg's "Grav&Cosmo", the
Lagrangian is well explained beginning on
pg.220. An interesting equation is simply,

dtau/dt = 1 - L , Eq.(9.2.2),

Let me call dtau = ds, then with a bit of
calculus find, (a good approximation)...
(using Eq.(9.2.2) above),
(dt/ds = 1+L , when L is small),

d^2(t) = dL ds , d^2(s)= -dL dt , Eq.(1)

and see how the time paradox developes using
the Lagrangian "L", in those.

The "ds" can be thought of as the uniform rate
at which a clocks ticks in CS k and likewise
for dt in CS K, and the d^2(t) and d^2(s) are
the accelerations of those clock *rates* as
"defined" by the change in the Lagrangian "dL".

Correct me if I'm wrong: In Newton Gravity, "L"
is constant so that dL=0 and dt^2 =0 because
both dt and ds are sync'd constant...tick, tick.

If I understand correctly, there is a subtle
variation in the Lagrange "L" , "dL" transforming
from Newton's theory to GR, wherein GR the L
is NOT constant.

A clearer notation, going forward, uses dt'=ds,
to provide Eq.(1) rewritten in a relativistic format,

d^2(t) = dL dt' , d^2(t')= -dL dt , Eq.(2).

As Peter pointed out, the L is in the dimension
of energy, so I'll rewrite Eq.(2) in terms of
increments to highlight Planck's constant "h",
as we evolve,

/\^2(t') = /\E' dt' , /\^2(t)= -/\E /\t , Eq.(3)

where /\E' = - /\E and

h = /\E' /\t' = /\E /\t is an invariant to yield,

/\^2(t') = h, /\^2(t) = -h , /\^2(t') = -/\^2(t) , Eq.(4) .

That find's Eq.(4) *quantizes* the "twin paradox".

Observers stationary in CS's K and K' will find the
variation of the Lagrangian results in a transfer of
time, such as the "second" via /\^2(t') = -/\^2(t),
with the time deduction applied to K, transferred
to K' , in relation to the excange of action.

[Ken S. Tucker]

On Sep 17, 3:21 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>

> >The following equation is ambiguous,
>
> >> g(Lx)^m'n' L_m'^m L_n'^n = g(x)^mn ?
>
> >I'd subject it to the rules of the "Einstein summation convention" AND
> >use the SIGMA summation too, to
> >make sure that is what you meant.
>
> ASCII is not nice, but there is no ambiguity. This equation is in every
> gtr text book, and at

Using summation convention, the LHS sums
over index's "m,n" and therefore on the RHS. That
is an abomdimation of symbolism, like A=+=-/x B.
There are procedures implied and explicit within
the mathematical symbolism.

What you can do is begin with,

g'_ab = (&x^u/&x'^a) (&x^v/&x'^b) g_uv

and see how to close to Peter's formula.
Regards
Ken S. Tucker

[The TimeLord]

Am Wed, 17 Sep 2008 15:56:08 -0700 schrieb "Ken S. Tucker"
<dyna...@vianet.on.ca> in
a4fa207e-346e-44d3...@q5g2000prf.googlegroups.com:

> On Sep 17, 3:21 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>>
>> >The following equation is ambiguous,
>>
>> >> g(Lx)^m'n' L_m'^m L_n'^n = g(x)^mn ?

[...]

> What you can do is begin with,
>
> g'_ab = (&x^u/&x'^a) (&x^v/&x'^b) g_uv

[...]

Without a context (evidently I missed out on something) it's difficult
to say, but it looks like the equation is trying to express the metric
in a moving frame under a Lorentz boost. Since the boost is Lorentz,
the metric has to be flat, otherwise the boost can not be Lorentz.

The following MACSYMA (Maxima) program expresses the idea:

/* Begin 'lorentz.mac' */
G:matrix([-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]);
L:matrix([gamma,-gamma*v/c,0,0],[-gamma*v/c,gamma,0,0],[0,0,1,0],[0,0,0,1]);
transpose(L).G.L;
subst(1/sqrt(1-v^2/c^2),gamma,%);
ratsimp(%);
/* End 'lorentz.mac' */

What you end up with is

matrix([-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1])

which is the same metric as in the rest frame (called "G"), thus showing
that the metric in the moving frame is the same as in the rest frame and
thus invariant under a Lorentz boost.

If space is curved, then the Lorentz boost does not apply, since it
assumes a priori that the space is flat.

--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!

[Ken S. Tucker]

Hi Timelord, what's your name?
Shall I call you Mr. Lord?
Thanks, I studied your post.

On Sep 17, 11:13 pm, The TimeLord <math-n-physics-...@att.com> wrote:
> Am Wed, 17 Sep 2008 15:56:08 -0700 schrieb "Ken S. Tucker"

> <dynam...@vianet.on.ca> in
> a4fa207e-346e-44d3-82aa-630c1cfba...@q5g2000prf.googlegroups.com:

>
> > On Sep 17, 3:21 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
> >> >The following equation is ambiguous,
>
> >> >> g(Lx)^m'n' L_m'^m L_n'^n = g(x)^mn ?
> [...]
> > What you can do is begin with,
>
> > g'_ab = (&x^u/&x'^a) (&x^v/&x'^b) g_uv
>
> [...]
>
> Without a context (evidently I missed out on something) it's difficult
> to say, but it looks like the equation is trying to express the metric
> in a moving frame under a Lorentz boost. Since the boost is Lorentz,
> the metric has to be flat, otherwise the boost can not be Lorentz.

Yes, you got it, all's well.

> The following MACSYMA (Maxima) program expresses the idea:
>
> /* Begin 'lorentz.mac' */
> G:matrix([-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]);
> L:matrix([gamma,-gamma*v/c,0,0],[-gamma*v/c,gamma,0,0],[0,0,1,0],[0,0,0,1]);
> transpose(L).G.L;
> subst(1/sqrt(1-v^2/c^2),gamma,%);
> ratsimp(%);
> /* End 'lorentz.mac' */
>
> What you end up with is
>
> matrix([-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1])
>
> which is the same metric as in the rest frame (called "G"), thus showing
> that the metric in the moving frame is the same as in the rest frame and
> thus invariant under a Lorentz boost.

If by the term "metric" you are referring to
the "metric tensor's" components such as g_uv
then, of course, they are NOT invariant and if
so that result is erroroneous.
The metric component transformation is subject to
"spatial contraction", "time dilation" and
"aberration".

Here's a 2 page brief you can try programming,
http://physics.trak4.com/modern-spacetime.pdf
It's a bit more complicated but I think it's
a necessary step to move to GR.

> If space is curved, then the Lorentz boost does not apply, since it
> assumes a priori that the space is flat.

Your probably right.

> // The TimeLord says:
> // Pogo 2.0 = We have met the aliens, and they are us!

Yup....

Regards
Ken S. Tucker

[Ken S. Tucker]

Hi Fred, and the other moderators ;-).

On Sep 20, 12:16 pm, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> Please note that SPF has a unique procedure for appealing posts that
> have been rejected by a moderator. If a poster receives a rejection
> notice via email, they can send an email to all the moderators at
> spf-ad...@stump.algebra.com appealing the rejection. The moderators
> will then discuss the reason for rejection and if any moderator thinks
> the original post should be approved, an email will be sent to the
> rejected poster informing them to resubmit the post. Sometimes, we
> might also request minor modifications to the original post to make it
> more acceptable.
>
> However, if the poster is using a munged email address to avoid spam,
> they will not get the rejection email message from our moderation
> system. And we have no way of changing the email address in our
> moderation software. If you are using a munged address, you can check
> to see if your post is rejected at,
>
> http://readystump.algebra.com/~spf/
>
> It will also show the reason for rejection at the bottom. PLEASE
> check this list before resubmitting a post that doesn't show up on the
> group. If your post was rejected, you can then appeal to the
> moderation board as mentioned above. I believe the "Rejected
> Messages" list is cleaned out every Saturday night so there could be
> some times where a poster might miss if their post was rejected or
> not. In that case, you can always just email the moderation board and
> ask if your post is not showing up on the group.
>
> Posters that continuously try to circumvent the proper appeal
> procedure by submitting the same rejected post many times will be
> considered for temporary or permanent blocking from posting to the
> group. We haven't had to do this to anyone yet, so your cooperation
> in this matter will be greatly appreciated. Thank you.
>
> Best Regards,
>
> Fred Diether
> Co-moderator sci.physics.foundations

Thanks for the heads-up Fred.
I think SPF has been a resounding success, especially
with it's global nature. Fred's on NA west coast, Jays
on NA East coast, Charles and Peter covering Europe.
Maybe we could get a couple of moderators to cover
the Austral-Asia sector of planet Earth, going forward.

I have other concerns. We all know that orientals have
made significant advances to theoretical physics, but
they have a linguist barrier since our group is mainly
English so I'm thinking of the possibilty of recruiting
moderator(s) in the western pacific.

Presuming the moderator meets the criteria of the
current moderators, that might be beneficial.
Regards
Ken S. Tucker

[Ken S. Tucker]

It's Sunday, I'll play along.

On Sep 21, 8:55 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Salviati <eckard.blumsch...@arcor.de>
>
> >Very nice and almost convincing. Nonetheless, I see unresolved very basic
> >questions in mathematics, e.g. Buridan's donkey closely related to seemingly
> >weird modern physics
>
> It is simply not meaningful to place a donkey with such accuracy. If one
> were to devise an experiment with some form of quantum analogue of the
> donkey, then one would expect a random result.

Butt Charles, you conject random can be rational,
which brings us back to "causality" related to true
randomness.
http://en.wikipedia.org/wiki/Buridan's_ass

Let's have a look at Tucker's ass instead.
To start, one pile of straw "A" is larger than the other "B"
by 1/2 my ass's mouth-full, and my ass bites the biggest
pile, that way my ass can start eating "A" at t=1.
1) A=B+1/2 , bite
2) B=A+1/2 , bite
3) A=B+1/2 , bite ....
evidently an oscillation.

Let's add in a caveat: *The fatter my ass becomes
the slower it moves from pile to pile*, OR alternatively,
*the smaller the piles get, the less motivated my ass
is to go to it*.
That would be a "red-shifting" of the oscillation.
1) A=B+1/2 , bite
2) B=A+1/2 , bite
4) A=B+1/2 , bite
8) B=A+1/2 , bite...

A similiar but subtlely different caveat: *As my ass
get's fuller, it takes smaller bites*,
1) A=B+1/2 , bite (1)
2) B=A+1/2 , bite (3/4)
3) A=B+1/4 , bite (1/2)
4) B=A+1/4 , bite (3/8)
5) A=B+1/8 , bite (1/4)
6) B=A+1/8 , bite (1/8) ....
The frequency of oscillation remains the same but
the amplitude of the bite decreases.
Using that, Tucker's ass will never starve, by using
Zeno's paradox. ((My study is funded by the SPCA)).

My point is, random is impossible in that paradox.
Regards
Ken S. Tucker
PS:SPF = Sci.Physics.Foundations

[Ken S. Tucker]

Hi fella's.
I'd like to examine the meaning of "force" in GR.

This 1st link gives a definition of 4-veloctiy "U^u".
http://en.wikipedia.org/wiki/Four-velocity#Components_of_the_four-velocity

Next we take the absolute derivative of U^u, w.r.t
"ds" that I'll denote as DU^u/ds,
http://en.wikipedia.org/wiki/Covariant_derivative#Derivative_along_curve

Next we generate a classical geodesic by setting
by setting absolute acceleration to DU^u/ds=0,
http://en.wikipedia.org/wiki/Geodesic#.28Pseudo-.29Riemannian_geometry

In view of this Christoffel,
http://en.wikipedia.org/wiki/Christoffel_symbol#Definition

I'll write the geodesic for a *circular orbit* as
(u=0,i , i=1,2,3) , to a 1st approximation as,

dU^i/ds = 1/2 (g_00,i - 2g_0i,0)

where the radius and theta (orbital angular momentum)
are constant, thus dU^i/ds=0 giving,

1/2*g_00,i = g_0i,0

and, in the radial direction,

1/2*g_00,1 = g_01,0 .

In view of Eq.(9) herein,
http://physics.trak4.com/modern-spacetime.pdf
we see the LHS = GM/r^2 (gravitational acceleration)
and the RHS = &V(orbital)/&t = inertial acceleration.

Next we can examine an object at rest on a planet.
The equation where DU^u/ds=0 and dU^u/ds=0 works
when an object is rest on the surface of the earth, but
we need to use g_uv = s_uv + a_uv to produce the
symmetric and antisymmetic components of the metric.

1/2*g_00,1 = g_01,0 = a_01,0

where a_01 = q*F_01, and F_01 =E(r)=Electric field(r),
to find
a_01,0 = q*&E/&t ==> EMR ==heat, (Power).

As a departure from free-fall occurs, a frictional force
is implied, to brake the free-fall. That renders an
accelometer reading to go non-zero, defined in a_01,0,
and outputs Power.

It checks well with GR, see,
http://physics.trak4.com/GR_Charge_Couple.pdf

In GR the physics is the same but absolute force
and acceleration vanishes.

[Ken S. Tucker]

Hi Kwan, Charles and fellow contributors
to this thread.

On Sep 22, 8:27 pm, qchiang <qchia...@yahoo.com> wrote:
> On 9月16日, 上午2时11分, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>
>
> > Thus spake qchiang <qchia...@yahoo.com>

>
> > >On 9_14_, __6_41_, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> > >> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
> > >Hi Charles,
>

> > >Thank you for your comments.
>
> > >Yes, this is still the same space. No new physics can be introduced.
> > >That is true. But, I am not trying to propose any fancy exotic
> > >physics. What I'm trying to point out is that the current physics is
> > >not complete for the Lorentz spacetime. The physics I'm introducing
> > >is a field which should have been identified along with Lorentz
> > >spacetime simultaneously.
>
> > >If you look at the PLANE ANGLE SPACE, you will notice each axis is a
> > >plane angle scale representing a whole plane, say xy-plane. A "plane
> > >angle rotation" from xy-plane to yz-plane IN THE PLANE ANGLE SPACE is
> > >a rotation of the whole xy-plane to the whole yz-plane. A physical
> > >field running from one whole plane to another whole plane is the kind
> > >of physics which should have been introduced along with Lerentz
> > >spacetime simultaneously. The function of such a physical field is to
> > >compare and make equivalent various plane angle scales in the same way
> > >EM field running in plane angles compares and makes equivalent linear
> > >scales. Neither linear nor plane angle scales can be defined
> > >arbitrarily as one wishes, but must be defined by real physical
> > >fields.
>
> > >This is what I mean that we have overlooked two symmetries in current
> > >Poincare group. The symmetry for the 3+1 Lorentz spacetime should be
> > >SO(6) (or isomorphism) and should be SO(10) for a 4+1 spacetime
> > >(please see my web sitewww.physicsrenaissance.comforthe 4+1
> > >spacetime) which is quite close to the observed particle spectrum.
>
> > I'm afraid the explanation doesn't make any sense. There is only one
> > space. Rotation in plane angle space has no meaning, except as an
> > ordinary rotation with a change of coordinates. An ordinary rotation of
> > 90deg about the y axis takes the xy plane to the yz plane. This is
> > already included in the Lorentz transformation. The discussion of
> > physical fields is misplaced, because we are talking of mathematical
> > transformations.
>
> > SO(6) is the group of rotations of 6 dimensional space. Rotations of 4
> > dimensional Euclidean space is SO(4). The restricted Lorentz group is
> > SO^+(1,3), because time appears differently in the metric.
>
> > Regards
>
> > --
> > Charles Francis
> > moderator sci.physics.foundations.
> > charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
> > braces)
>
> >http://www.teleconnection.info/rqg/MainIndex-隐藏被引用文字 -
>
> > - 显示引用的文字 -
>
> Hi Charles,
>
> Thank you for your comments. Here are some explanations:
>
> We can define the scale of a linear axis at wish and that of another
> axis at wish. The two scales won't match unless they are defined by
> certatin physical objects, such as a yard stick, or light speed, or
> magnetic field lines, etc. Currently, we may say the accurate
> "linear" scales is defined by electromagnetism.
>
> Your view that "An ordinary rotation of 90deg about the y axis takes
> the xy-plane to the yz-plane. This is already included in the Lorentz
> transformation." relies on the fact that the plane angle scales on xy-
> plane matches that on yz-plane.
>
> The solid angle rotation (and the physical field making that
> rotation), or the plane angle rotation in the PLANE ANGLE SPACE:
>
> - makes equivalent various plane angle scales, degree to degree, 10 to
> 10, 300 to 300, 900 to 900, 3600 to 3600.
> - hence also makes an arbitrary finite plane angle on any plane
> uniquely decomposable into plane components,
> - and hence preserves the value of any finite plane angle when
> observation frame is changed.
>
> xy-plane may make ordinary rotation to the yz-plane according to
> Lorentz transformation, but the two plane angle scales are not
> guaranteed to match if the physical field making above solid angle
> rotation doesn't exist. This is similar to the fact that, without
> electromagnetic field running between all linear axes, linear scales
> wouldn't be equivalent and a line element cannot be preserved under
> rotation.
>
> But "An ordinary rotation of 90deg about the y axis takes the xy-plane
> to the yz-plane" still compares 1mm to 1mm, 1 meter to 1 meter. It
> doesn't compare degree to degree, 10 to 10, 300 to 300, 900 to 900,
> 3600 to 3600.

The background of the LT is traceable to the invariance
of a spherical output of light being spherical relative to
all CS's, such that,

(ct)^2 = x^2 + y^2 +z^2

is true in all CS's moving relatively to source of the light.
That evolved to become in GR,

ds^2 = 0 = g_uv dx^u dx^v , {u,v = 0,1,2,3},

where light is concerned.

The above defines how a sphere of light is generated
in SR and then GR.

In g-fields (and perhaps EM-fields) the spacetime is
non-orthogonal, meaning, x,y,z can NOT be assumed
to be capable of being set at 90 degree angles.

To interface with Kwan's math, rotating a CS 360 degrees
about either x,y or z will not return the vectors to their
original positions. Perhaps unit vector "i" will end up at
359, unit "j" and 361 and unit "k" at 360, all because
the Circumference=2*pi*Radius does NOT hold in a
space subject to a g-field.
The math is tricky, but verified by the variation of
Mercury's orbital perihelion advance.

>Some people don't feel like to view it in a philosophical way.
> However, he may still see the same thing from mathematics. The form
> of the Casimir invariant also suggests a new symmetry on top of the
> plane angle rotation, which has always been overlooked.
>
> That the direct rotation from plane to plane for a 3+1 Lorentz
> spacetime would be SO(6) (or isomorphism) is because there are 6
> planes. Each plane needs be defined equialent to every other plane.
> And hence a separate physical field is needed to run between every
> pair of planes.

In GR 1916 (online), Eq.61 there are 6 EM field rotations,
F14, F24, F34, F12, F23, F31, that I think induce non-
orthogonal spacetime.
Regards
Ken S. Tucker