On Wednesday, November 17, 2021 at 3:09:39 PM UTC-8, Thomas 'PointedEars' Lahn wrote:
> patdolan wrote:
>
> > Critical Theory comes in several flavors: Critical Law Theory, Critical
> > Literature Theory, Critical History Theory, Critical Race Theory. To
> > these we now add Critical Relativity Theory!
> >
> > In the spirit of Derrida we shall deconstruct the clumsy reasoning of
> > special relativity
> LOL.
> > and separate said reasoning from the algebraic symbols and equations
> > that express it,
> Since it is fundamentally based in geometry, namely frames of reference
> which can understood as (moving) coordinate systems, that approach is
> hopeless.
> > keeping in mind that mathematics is just another form of rhetorical
> > expression wherein falsity can be expressed every bit as plausibly
> > as the truth.

> Not true. Natural language is ambiguous and rather loose; it is why
> (despite knowing logic) it is so easy to commit fallacies using natural
> language. Mathematics, in its symbols, terms, and reasoning is (given a
> context) unambiguous and unforgivingly strict.

1^4 = i^4

sqrt[ 1^4 ] = sqrt[ i^4 ]

+/-( 1^2 ) = +/-( i^2 )

+/-( 1 ) = +/-( -1 )

+/- 1 = -/+ 1

>
> In the words of Richard Feynman:
>
> ‘You might say, “All right, then, there’s no explanation of the law;
> at least tell me what the law is — why not tell me in words instead of
> in the symbols?

I did this. See MUONS, SCHMUONS! at the bottom of my post. Read through it slow, Long Ears. Then take up my challenge if you dare: Prove that relativity provides only one and unique answer for the elapsed time on the lab clock. I can assure the world and posterity that you can't and won't do prove one, unique time.

Mathematics is just a language, and I want to be able
> to translate the language." And, in fact, I can — and with patience,
> I think I partly did. I could go a little further and explain more
> detail — that this means if it’s twice as far away the force is
> one-fourth as much, and so on — and can convert all these into words.
> I would be, in other words, kind to the layman, as they all sit, hopeful
> that you will explain something. Various different people get different
> reputations for their skill at explaining to the layman in layman’s
> language these difficult and abstruse subjects.
>
> The layman then searches for book after book with the hope that he will
> avoid the complexity which ultimately sets in, even by the best expositor
> of this type. He reads the things, hoping — he finds, as he reads, a
> generally increased confusion, one complicated statement after the other,
> one difficult-to-understand thing after the other, all apparently
> disconnected from one another — and it becomes a little obscure, and
> he hopes that maybe in some other book there’s some explanation which
> avoids — I mean, the man almost made it, you see — maybe another fellow
> makes it right.
>
> I don’t think it’s possible, because there’s another feature: mathematics
> is not just a language; mathematics is a language plus reasoning; it’s
> like a language plus logic. Mathematics is a tool for reasoning. It’s in
> fact a big collection of the results of some person’s careful thought and
> reasoning. […]’
>
> <https://www.feynmanlectures.caltech.edu/fml.html#2>
> > “There is only the text.”— J. Derrida
> LOL.
> > According to special relativity two observers in motion with respect to
> > each other will disagree on each other’s length. They will also disagree
> > on the proper flow of time. But they will always agree on the velocity
> > they have with respect to one another.
> No, the velocity that observer A ascribes to observer B is necessarily the
> arithmetic inverse of the velocity that observer ascribes to observer B,
> provided that they are both looking in the same direction and choose their
> coordinate systems such that the positive part in on the same (usually
> right-hand) side.
>
> > This is exceedingly strange.
>
> There is nothing strange about it.
> > How can it be that two relative quantities, space and time, combine to
> > produce an absolute quantity called relative velocity?
> It is not absolute at all. If it were absolute, then every observer would
> assign the same velocity to the same object, regardless of their relative
> state of motion. The very point of the theories of relativity is that this
> is not so.
>
> However, if you consider the relevant equations of the (inverse) Lorentz
> transformation for relative (inertial) motion *only* along the x-axis,
>
> t = γ (t' + v/c² x')
> x = γ (x' + v t'),
>
> where for simplicity we say that v would be the velocity (usually just a
> speed, but this particular motion is one-dimensional) that an observer that
> we define as stationary would assign to a clock that, at rest in its own
> frame shows time t, then you can see that for the temporal interval
>
> Δt = γ (Δt' + v/c² Δx') = γ Δt'
>
> and for the spatial interval
>
> Δx = γ (Δx' + v Δt') = γ v Δt',
>
> then the velocity of that moving clock for the stationary observer is still
>
> Δx/Δt = v.
>
> Similarly for an observer at rest in the "moving" frame, when they are
> talking about a clock that is at rest in the stationary frame, they
> transform the coordinates by the (original) Lorentz transformation
>
> t' = γ (t − v/c² x)
> x' = γ (x − v t),
>
> – you can obtain that by solving the equations for the other quantity, not
> just by arbitrary substitution – which for (their) time intervals becomes
>
> Δt' = γ (Δt − v/c² Δx) = γ Δt
> Δx' = γ (Δx − v Δt) = −γ v Δt.
>
> Then the velocity that they assign to the stationary clock is
>
> Δx'/Δt' = −v,
>
> as we would expect.
> > It is true that SR does have a formula for calculating coordinate
> > velocity; just like it has formulas for calculating coordinate space
> > and coordinate time. But the Einstein velocity addition formula ONLY
> > applies to a third object in motion wrt a pair of FoRs.
> But the second FoR is implied when we are talking about a velocity. There
> has to be some frame of reference relative to which we are defining the
> value.
> > If that third object happens to be at rest wrt one of the FoRs then
> > Einsteinian velocity reduces to Galilean velocity,
> Yes, but that is a rather pointless statement because “at rest” means that
> the relative velocity is zero.
>
> It is more useful to realize that as one of the relative speeds *approaches*
> zero the composed velocity *approaches* the Galilean term:
>
> u(v, u') = (v + u')/(1 + v u'/c²)
>
> lim_{v u' → 0} u(v, u') = v + u',
>
> as v u'/c² → 0 then due to the large value of c.
>
> [This equation did not simply fell out of the sky. It is, again, a
> (mathematical) *consequence* of the Lorentz transformation, and Einstein
> derives it in “On the Electrodynamics of Moving Bodies” (1905). I have
> also derived it here many times.]
> > albeit subject to the speed limit c.
> That is a contradiction in terms.
> > Relativists simply assumed without further justification that if FoR-1
> > measures a velocity v between itself and FoR-2 then FoR-2 must measure
> > the same numerical value v for the velocity between itself and FoR-1.
> No.
> > Einstein’s choice to make velocity strictly Galilean when calculating the
> > velocity between pairs of FoRs ( yes, it is a choice because it does not
> > follow from either the first or the second postulates ) can be expressed
> > mathematically as
> >
> > ∆x’/∆t’ = ∆x/∆t = v (1)
> Wrong, see above.
> > I now raise equation (1) to the level of a postulate and declare it to be
> > the third, and heretofore hidden, postulate of special relativity.
> But you do not understand special relativity correctly (yet).
> Your/an argument/conclusions from your ignorance is a useless fallacy.
>
> > [tl;dr]
>
>
> PointedEars
> --
> “Nature uses only the longest threads to weave her patterns
> so that each small piece of her fabric reveals the organization
> of the entire tapestry.”
> —Richard Feynman, theoretical physicist, “Messenger Lecture” 1 (1964)

Thomas, I have no interest in debating the algebra with you. You are not appreciating the meta-algebra involved. Nor will you anytime soon. Just address the MUONS, SCHMUONS! challenge. Or go silent. You have always been a second stringer in this forum.