Groups > sci.physics.relativity > #668143

Re: Hidden dimensions could explain where mass comes from

From	Thomas Heger <ttt_heg@web.de>
Newsgroups	sci.physics.relativity
Subject	Re: Hidden dimensions could explain where mass comes from
Date	2026-01-10 09:24 +0100
Message-ID	<mseg9dFd8rjU4@mid.individual.net> (permalink)
References	(11 earlier) <ms969bFglcaU1@mid.individual.net> <yFidnSRveJvwRcL0nZ2dnZfqn_udnZ2d@giganews.com> <10jpn72$1j3dn$1@gwaiyur.mb-net.net> <skGdnUBXqp-34f30nZ2dnZfqnPadnZ2d@giganews.com> <dhmdnUS-Gqf6PP30nZ2dnZfqnPSdnZ2d@giganews.com>

Show all headers | View raw

Am Freitag000009, 09.01.2026 um 07:34 schrieb Ross Finlayson:
> On 01/08/2026 07:55 PM, Ross Finlayson wrote:
>> On 01/08/2026 05:55 PM, Thomas 'PointedEars' Lahn wrote:
>>> Ross Finlayson wrote:
>>>> The idea that everything physics is always parameterized
>>>> by time or 't' is often formalized "the Lagrangian",
>>>
>>> No, the parametrization by time is a concept in Lagrangian _mechanics_
>>> which
>>> is based on the _principle of stationary ("least") action_.  The
>>> action is
>>> defined as
>>>
>>>    S[x(t)] = ∫ dt L[x(t), dx(t)/dt, t],
>>>
>>> where x may be a vector (field), and L is the Lagrangian (function).
>>> [Both S and L are *functionals*: they depend on a function, x(t);
>>> hence the customary notation with rectangular brackets.]
>>>
>>> In special relativity, one finds from the Minkowski metric
>>>
>>>    ds^2 = c^2 dτ² = c^2 dt^2 - dx^2 - dy^2 - dz^2
>>>                   = c^2 dt^2 [1 - (dx/dt)^2 - (dy/dt)^2 - (dz/dt)^2]
>>>                   = c^2 dt^2 (1 - V^2/c^2)
>>>
>>> that
>>>
>>>    S[x] = -m c ∫ ds = -m c ∫ dt c √(1 - V^2/c^2)
>>>                     = ∫ dt [-m c^2 √(1 - V^2/c^2)],
>>>
>>> where the prefactor -m c is introduced so as to produce a quantity with
>>> dimensions of action (energy × time, cf. ℎ and ℏ) and the correct
>>> canonical
>>> momentum [*], and in the integrand one with dimensions of energy; so the
>>> relativistic non-interacting Lagrangian is
>>>
>>>    L = -m c^2 √(1 - V^2/c^2) = -m c^2 √[1 - (dX/dt)^2/c^2].
>>>
>>> It turns out that this leads to the correct energy--momentum relation,
>>> as I pointed out earlier.
>>>
>>>    [*] For example, the canonical 3-momentum is, from the Euler-- 
>>> Lagrange
>>>        equations
>>>
>>>          0 = d/dt ∂L/∂(dX/dt) - ∂L/∂X = d/dt ∂L/∂V - ∂L/∂X = d/dt ∂L/∂V
>>>
>>>          P = ∂L/∂V
>>>            = -m c^2 ∂/∂V √(1 - V^2/c^2)
>>>            = -m c^2/[2 √(1 - V^2/c^2)] ∂/∂V (1 - V^2/c^2)
>>>            = -m c^2/[2 √(1 - V^2/c^2)] (-2 V/c^2)
>>>            = m V/√(1 - v^2/c^2)
>>>            = γ(v) m V.
>>>
>>>    [It is interesting to note that this way the relativistic/exact
>>> 3-momentum
>>>     for a massive particle can be derived purely from the Minkowski
>>> metric,
>>>     without a Lorentz transformation (but the Minkowski metric is
>>> Lorentz-
>>>     invariant, somewhat by design [I showed before that you do not even
>>>     need to assume Lorentz invariance to derive it, just a constant 
>>> speed
>>>     with which information propagates in space)].
>>>
>>> Since from the above follows that ds = c dτ, one can also write
>>>
>>>    S[x(τ)] = -m c ∫ dτ c = -m c^2 ∫ dτ.
>>>
>>> The physical paths of free motion, which (one can prove) are spacetime
>>> geodesics, are those where the action S[x(t)] is minimal (stationary in
>>> general).  From the form above one can see that those are the
>>> trajectories W
>>> along which the elapsed proper time ∆τ = ∫_W dτ is maximal, which is
>>> another
>>> way of describing "time dilation" when there is relative motion, and
>>> finally
>>> explaining the "twin paradox" as nothing more than a consequence of
>>> different elapsed proper times along different worldlines.
>>>
>>> One can also see here that mass arises naturally from assuming the
>>> principle
>>> of stationary action.
>>>
>>>> sort of like "the Machian" is a usual notion of far-field.
>>>
>>> No, nonsense.
>>>
>>>> [pseudo-scientific word salad]
>>>
>>> You are a hopeless case.
>>>
>>
>> So, parameterized by time then, like I said,
>> like Lagrange says.
>>
>> You mention least action and it's a pretty reasonable
>> principle, where the theory is sum-of-histories sum-of-potentials
>> least-action least-gradient a continuum mechanics, that
>> obviously enough it's a field theory.
>>
>> You know, momentum isn't very much conserved in kinematics.
>> It sort of adds up for each of the ideal equal/opposite
>> inelastic interactions, yet any sort of rotation loses it.
>>
>>
>>
>> Much like "whatever satisfies the _Lorentzian_ is a model
>> of relativity", there's that "whatever satisfies the
>> _Lagrangian_ is a model of relativity with a clock hypothesis".
>>
>>
>> Perhaps you might be familiar with the notion of "implicits",
>> for example that "x" is "x(t)" and forces are always implicitly
>> functions of time, t, and so on.
>>
>> Forces are functions of time, ....
>>
>> Then, besides that logic demands a temporality else
>> it's readily demonstrable as false, time the usual
>> parameter t is an implicit.
>>
>> Implicits may remind
>> of "running constants", then for example about notions
>> like the monomode process, since usually accounts as
>> after the _Laplacian_, the sum of 2'nd order partials,
>> the _Lorentzian_, the sum of 2'nd order partials x +- t,
>> and whether that's zero or off-zero, non-zero.
>>
>> The differential d and partial-differential little-greek-d
>> are two different things, your Lagrangian L is already
>> second-order in d^2 t while velocity V is only first
>> order, then taking their partials w.r.t. each other,
>> finds that now what was taken as the root of the square,
>> gets issues with the nilpotent and nilsquare, about
>> the off-zero case, helping explain why what falls out
>> as a linear expression or in simple terms,
>> ignores part of its own derivation there.
>>
>> Otherwise it's quite plainly Galilean, one may note.
>> (Eg, any "unboundedness as infinity".)
>>
>> Meeting the form, ....
>>
>>
>>
>> Yeah, it seems quite so that the larger reasoners
>> very well appreciate the contents of that "T-theory,
>> A-Theory, theatheory" thread.
>>
>> Including its logical elements, its mathematical elements,
>> and otherwise its canonical and novel elements, so relevant.
>>
>> Then also for physics.
>>
>>
>>
>> It seems the action S is simply contrived to dump out
>> the usual definition, as it is, "timeless", and absent
>> moment, of momentum the linear since Lagrange.
>> Being that it's just "defined".
>>
>>
>>
>> "Implicits" is what's involved, since whatever then
>> results in the derivations cancelling themselves away,
>> perfectly model Lagrangians, Lorentzians, ..., Laplacians,
>> a hollow shell.
>>
>>
> 
> 
> When encountering various fields of mathematics,
> when the only tool there is is a hammer then
> everything looks like a nail, yet, in a world of
> nails, many varieties of hammers will do.
> 
> So, when learning about things like "the operator calculus"
> and "functional analysis" it's a pretty great thing,
> first for treating the differential as operators,
> yet it's really quite an overall approach to things.
> 
> Now, the definition of "function" is one of the most
> fluid definitions in mathematics, or it has been over
> time. For example "classical functions", then those
> after "classical constructions", then about whether
> asymptotes are admitted, about the continuous, about
> the differentiable and C^\infty and so on, about
> whether Differential Geometry has gone backward and neither
> tangents nor normals asymptotes, then whether "functionals"
> are "functions" and for example from probability theory
> whether "distributions" are "functionals" or "functions",
> "functionals" live under functional analysis thus an
> operator calculus, while "functions" get all involved
> the usual relations about since there not being division
> by zero, though the meromorphic and symplectic and
> many other usual translations make for a resulting
> sort of "free analysis on the plane", where pretty much
> any sort of parameterized form like that of a circle,
> can be treated as a function or piecewise as a function.
> 
> So, they're functions.

I use the word function similar to how it is used in programming.

A function is therefore a 'mathematical machine', which swallows input 
and produces output of some kind.

The output is NOT a function, because that would create two different 
meanings of the same word 'function'.

E.g.:

  if you have a function named -say- 'f', then f(x) is not a function, 
but the output of the function 'f' from input 'x'.


TH

Thread

Hidden dimensions could explain where mass comes from Anthk NM <anthk@disroot.org> - 2026-01-04 14:47 +0000
  Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-04 15:41 +0000
    Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 17:06 +0100
    Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-04 15:08 -0800
      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 10:47 +0100
        Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-05 07:59 -0800
          Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-05 08:22 -0800
          Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:43 +0100
            Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 00:00 -0800
              Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 09:28 -0800
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 10:04 -0800
            Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 10:43 +0100
              Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 06:51 -0800
          Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:22 +0100
        Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 14:10 -0800
          Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:36 +0100
          Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:45 +0100
          Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 23:49 +0100
            Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 15:09 -0800
              Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 15:14 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 00:47 +0100
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-05 19:40 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 17:29 +0100
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 08:48 -0800
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-06 17:29 -0800
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-06 19:20 -0800
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-08 23:20 -0800
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-09 00:03 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-07 08:47 +0100
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-07 11:46 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-08 09:03 +0100
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 08:16 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-09 02:55 +0100
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 19:55 -0800
                Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-08 22:34 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:24 +0100
                Lagrangian mechanics (was: Hidden dimensions could explain where mass comes from) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-09 12:13 +0100
                Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 08:37 -0800
                Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 09:03 -0800
                Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-12 07:58 -0800
                Re: Lagrangian mechanics nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-09 21:17 +0100
                Re: Lagrangian mechanics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-09 13:23 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:13 +0100
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-08 20:13 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-10 09:19 +0100
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-10 13:08 -0800
                Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-11 10:13 +0100
              Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 00:45 +0100
                Re: Hidden dimensions could explain where mass comes from "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-10 13:12 -0800
  Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-04 17:07 +0000
    Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 18:39 +0100
    Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-04 18:41 +0100
    Re: Hidden dimensions could explain where mass comes from Anthk NM <anthk@disroot.org> - 2026-01-05 20:11 +0000
      Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-05 20:52 +0000
        Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:36 +0100
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:38 +0100
      Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:03 +0100
      Re: Hidden dimensions could explain where mass comes from Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-05 22:26 +0100
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 22:55 +0100
    Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-09 14:06 +0000
      Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-09 21:31 +0100
  Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-04 20:46 +0100
    Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-04 13:54 -0800
      Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-04 14:45 -0800
    Re: Hidden dimensions could explain where mass comes from athel.cb@gmail.com <user12588@newsgrouper.org.invalid> - 2026-01-05 10:18 +0000
      Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-05 18:32 +0100
  Re: Hidden dimensions could explain where mass comes from Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:06 +0100
    Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 10:43 +0100
      Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 06:50 -0800
        Re: Hidden dimensions could explain where mass comes from nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 16:12 +0100
          Re: Hidden dimensions could explain where mass comes from Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 07:47 -0800
  Re: Hidden dimensions could explain where mass comes from ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-06 18:00 +0000
  Re: Hidden dimensions could explain where mass comes from Richard Hachel <rh@tiscali.fr> - 2026-01-11 22:32 +0000

csiph-web