Re: Neutrino Mass and Supernovae

From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 10/12/04 

Date: 12 Oct 2004 12:46:09 -0700

Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<ckgb48$jcg$1@news.urz.uni-heidelberg.de>...
> Ken S. Tucker wrote:
> > Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<ckdkr6$6hp$1@news.urz.uni-heidelberg.de>...
> >
> >>Ken S. Tucker wrote:
> >>
> >>>Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<ck8ele$kub$1@news.urz.uni-heidelberg.de>...
> >
> > ...
> >
> >>>google "w.w.sawyer" >1000 hits.
> >>>((worked together from 1968))
> >>
> >>Thanks. Giving his name would have been enough.
> >
> >
> > Well if you have a chance you should read his ideas,
> > I didn't fully appreciate his help, I was a 15 year
> > old brat. I was using balloon membranes and drawing
> > graphs on them and then streching them to study Grad
> > Div and Curl, in LT and GR. We had some very interesting
> > conversations.
>
> You learned GR already at the age of 15??? Wow.

Of course not, I'm still learning GR! Any kid with
a science slant can understand 90% of GR's concepts.
Unfortunately, the mathematical description of those
concepts is complex. I got hung up on curl, ds, and
energy density.
  Sawyer was really helpful with vector calculus and
SR. He had some issues with ds, and stated quite
frankly "no one really understood it". He suggested
a nonorthogonal approach might be necessary, and I
eventually finalized on U_i=0 in the mid 70's. It's
rather insignificant because it's complicated and
doesn't lead immediately to any no predictions, IOW's
it's an opinion.
 
> >>>>And did this Prof also say this stuff about "u_j=0 in GR",
> >>>>and that this means that "absolute velocity vanishes", and that
> >>>>a Lorentz boost is a translation, and that Lorentz boosts are not
> >>>>allowed in GR?
> >>
> >>I notice that you did not answer this question below.
> >
> >
> > No, I was detailed a problem, that is my solution.
>
> "Detailed" by whom? By this Prof. Sawyer?
>
> Did you ever check the solution with someone knowledgeable?

Certainly, it was refereed.
 
> >>>Either you do not understand the problem or you don't take it
> >>>seriously, let me explain.
> >>>
> >>>From the standpoint of mathematics a displacement like
> >>>
> >>> ds^2 = g_uv dx^u dx^v
> >>>
> >>>does NOT diffentiate between relative and absolute motion,
> >>>and neither do mathematicians, it's a an equation without
> >>>regard to the nature of the relativity imposed on FoR's.
> >>
> >>You do not make any sense. The equation above has nothing to
> >>do with motions! It only defines the *geometry* of a space
> >>- i.e. it tells you how lengths and angles are defined!
> >
> >
> > In geometry, ds^2 is regarded as a displacement in the
> > context of spacetime.
>
> Yes. So what? That still has nothing to do with motion.
 
> >>>In fact relative motion is a subset (or group) of all
> >>>possible motions in all "proper" CS's. I take the ds^2
> >>>above to be the generic representitive set defining all
> >>>possible displacements, including absolute and relative
> >>>displacements.
> >>
> >>Care to explain what exactly the difference is? What do you
> >>*mean* when you say "absolute displacement"?
> >
> >
> > Generally speaking, any CS that permits dx_i dx^i =/=0
> > allows "absolute displacement", and that is NOT a
> > permissable CS where relativity is imposed.
>
> I notice that you did not answer my question what you mean
> by "absolute displacement".
>
> BTW, *why* is a CS in which dx_i dx^i =/= 0 not permissable?

That's our/my answer, reread.
 
> >>>In physics the u,v are conventionally set to integer
> >>>values 0,1,2,3, where "0" is messaged to being the
> >>>dimension of time.
> >>>
> >>>The ISU has agreed L=ct,
> >>
> >>ISU? From the context, perhaps International System Unit?
> >
> >
> > Yup, I work strictly in ISU guidelines.
> > ...
>
> Nice. Then why did you bring up inches in another post?

Ha, it sounded better than toenail length, using inches
was a classier example of an arbituary unit.
 
> >>>Problem...
> >>>
> >>>define the *relative* displacement subset of
> >>>
> >>> ds^2 = g_uv dx^u dx^v.
> >>>
> >>>within the above conditions expressed generally
> >>>covariantly, and prove.
> >>>
> >>>Solution U_i =0 defines the theory of relativity,
> >>>in all FoR's.
> >
> >
> >>>Proof, Invariant Mass = (rest mass)*gamma.
> >>> experimentally verified by nuclear tests.
> >>
> >>1) Invariant mass = rest mass, exactly. (rest
> >>mass)*gamma = *relativistic* mass, not invariant mass!
> >
> >
> > Simply put, your suggestion that rest mass, applicable
> > in one CS is invariant for all CS's is wrong.
>
> <http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/mass.html>
> Quote:
> "The invariant mass is therefore often called the "rest mass"."

Discussed in another thread.
 
> >>2) That has nothing at all to do with U_i = 0 defining the theory
> >>of relativity.
> >
> >
> > It certainly does! All momentum covariant tensors like p_i
> > vanish
>
> What are "momentum covariant tensors"? I know only the momentum four-vector.

Well if U_i =0 (3-velocity) then momentum p_i=0 (not the energy given
by p_0). Since p_i=0 it follows

  p_0 = rest mass,

and is NOT invariant.
 
> > The relativity condition
> >
> > U_i =0
> >
> > is extremely powerful.
>
> For which object is this equation supposed to hold?

It is true for any object and all objects.
 
> > Try it, tell me where it fails.
>
> It fails as soon as I consider the four-velocity of an object moving
> with respect to me.

Then you are welcome to use absolute displacements.

> >>>The Lorentz boost is meaningless in GR.
> >>
> >>Please support that assertion.
> >
> >
> > Well, if you end up with a partial like &t'/&x
> > dependant upon a finite spacetime displacement you've
> > imported a translation into the transformation.
>
> Well, since for a Lorentz boost, &t'/&x does *not* depend
> on a "finite spacetime displacement" (as I said repeatedly,
> it is simply -beta gamma), I do not see why you
> think a Lorentz boost is a translation.

This is circular, is your "-beta gamma" a constant?
 
> > In simple tensor analysis transformations are meaningful
> > only at a point.
>
> That would be news to me. Where did you get this from?
> What about the *example* for a coordinate transformation (for the
> Schwarzschild solution) which I mentioned in another post?

If you must ask you really do not understand tensor
analysis, or transformations, learn the meaning of

  dx'^u = (&x'^u/&x^v) dx^u

especially in GR.
 
> > More advanced treatments that include
> > nonsymmetrical g_uv require a finite in accord with the
> > ISU.
>
> What on earth has this to do with the ISU?

L=cT
 
> > Because Time is independent of length, &T'/&x =0 just
> > as &T/&x =0, I work within ISU standards.
>
> Time in coordinate system S' is *not* independent of length in
> coordinate system S!

Minkowski states clearly T and T' may be parallel,
hence in that group &T'/&x=0 as does &T/&x=0, and U_i =0.

What U_i=0 does is set the time axes T and T' to be parallel,
neat eh. If you think about light cones, you'll see that is a
necessary condition in "relativistic" spacetime.
 
####
> >>Oh, BTW: if I am a kook, how did I manage to obtain a PhD in physics?
> >>Working in Quantum Field Theory, where a good understanding of SR and
> >>tensor analysis is required?
 
> > Bjoern, even a superficial acquaintance to QFT requires
> > some analysis of Shapiro's experiments, as it relates to
> > length in fields.
>
> You did not answer my question.

You placed two ? marks in the statement #### above, so I
presumed you don't know the answers, OR the questions
were rhetorical. Evidentally the questions were not
rhetorical and you do not know the answers, but expect
me to know or even care.
  One of the best theoreticians I met described himself
as an "electrician". I regard myself as a "technician",
because a technician usually needs to understand the
theory better than the theoretician who invented the
theory that needs to be fixed by the technician:)

Regards
Ken S. Tucker

 
> Bye,
> Bjoern

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