Jorrie wrote:false arguments
The numbers work! The interval equation (
X² = I² + T²) and energy equation (
E² = m² + p²) are analogous. Further, a mass triangle and Einstein's energy triangle must agree, by mass-energy equivalence.
Jorrie wrote:The problem is that space-time is not Euclidean.
I didn't say it was. But Einstein's light clock and energy triangles
are Euclidean! That should be sufficient to question naïve acceptance of archaic space and time coordinates to represent the continuum.
Fortunately, we aren't stuck with clumsy spacetime. It has legacy value but it's not taking us anywhere
new. As you've informed us, physics also employs
light cone coordinates, which entail lightlike and spatial coordinates. It's slowly catching up to my combination of lightlike and temporal coordinates, Times Square (
T2).
Jorrie wrote:[Your] confusing terms like "radiant energy (p)" and "light interval (I)" ...are creating complete confusion. Neither ... have the meanings in physics that you attempt to attach
I'm sorry about any confusion. "
Radiant energy" is nothing special.
Taylor & Wheeler use it for kinetic energy, particularly in the case where a "particle" has zero rest mass. Such
radiant energy transmits via lightlike intervals.
We also know
radiant energy as the "
momentum component" (pc)* of the total energy, even for massive particles. An equivalent term would be"
radiant mass".
*just p in natural units, where
c=1
Jorrie wrote:Never heard of "mass charge" - what's that?
As I consider energy to be the more fundamental aspect of mass-energy. "
Mass charge" is
energy in any form. It could also be called "
inertial charge" or "
gravitational charge" by the equivalence principle. I meant to invoke both latter terms with the former.
Jorrie wrote:Please also define "instance of a field (G or EM)" in standard terms (or at least provide a reliable reference).
An
instance of a particle should be understood to be an event along that particle's worldline, i.e. the particle
at a particular instant. Each
instance of a particle has an associated future light cone, which defines the entirety of its potential causal interaction. That future light cone corresponds to an
instance of that particle's field.
A field is a region of
potential force pairing (e.g. potential
interaction with a test particle.). As QED sees
forces mediated by massless force carriers, an
instance of a field is the future light cone of a particle. It is the collection of all potential
forces, which can originate from an instance of a particle.
Jorrie wrote:What is a "lightlike field element"?
"
A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex... in the case of half-lines, it extends infinitely far. ... The definition of a cone may be extended to higher dimensions." Let the
half lines (i.e.
rays) be "radial elements". A
lightlike field element is a radial element of a future light cone (in 4D).
A more elegant and insightful definition is that a lightlike field element is an
unpaired force. This sees force as an object, not unlike its conventional treatment as a vector. I model a force (i.e.
field element) more fundamentally, as a
particle-
interaction worm
hole (
pinhole). With chronaxial spin, a particle's field is generated.
Jorrie wrote:And "chronaxial spin" has been refuted by Lincoln, myself and others in the past. Why are you persisting with it?
1. You're too intelligent to continue denying one of four available, independent spin axes.
2. It's the least I can do, considering all I've learned from you.
3. With all due respect, said refutations have been insubstantial. (Remind me, if there was a good one.)
4. Chronaxial* spin is the
best and
only available explanation of quantum spin. QM is woefully incomplete without it.
*More generally, it occurs about a particle's worldline, which parallels proper time in the particle's rest frame.
Jorrie wrote:["relativistic mass"] has been simplistically derived by Einstein, in its energy form.
Good for him! My feeling is that length contraction, time dilation and relativistic mass-energy all occur together and if the light clock example gives us one, it should give us all three.
Jorrie wrote:I think your next diagrams really an Epstein space-propertime diagram, which never caught on due to its confusing mixing of "my space" and "your time".
Yes! My post included a link to
Epstein diagrams. He and Minkowski both suffer with spatial coordinates. The simplicity of Epstein diagrams is retained by replacing spatial with
invariant lightlike coordinates,
agreeable to
all observers. As I showed, the geometry is as elegant as with the light clock.
Jorrie wrote:...you are talking inertial movement here, there are no "moving clocks" ... each clock 'run's slow' according to the others perspective. It is just an observational perspective.
Those are
equally legitimate "observational perspectives", wrt physical law. As you know, SR allows no privileged inertial frames. There was nothing about Einstein's light clock example nor my analogous diagram that would deny reciprocal perspectives. In fact, that helps legitimize them.
Jorrie wrote:no clock has "more instances of its field". It is only the perception of the "other guy".
I beg to differ. We
agreed that gravity is relative. I now provide a mechanism.
Two stacks of coins oriented at an angle to each other, each think the other stack has more coins per its own vertical measure. Do the same for instances of a gravitational field along angled worldlines and you've got relative gravity.
- Parallel lines from either stack measure higher coin counts in the other angled stack. Parallel simultaneities measure mutually higher temporal densities of gravitational fields in different inertial frames.
Length,
duration and
mass (inertial
and gravitational) are indeed frame dependent. I take that as the meaning of "relative" in SR. Additional terms like "reciprocal" and "mutual" apply but are redundant.