On Saturday, October 9, 2021 at 2:13:01 PM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 4, 2021 at 11:02:16 PM UTC-7, Richard Hertz wrote:
> > If you don't like revisions of historic papers, please stop reading.
> >
> > This post is about fallacies and circular reasoning present in the 1905
> > paper "Does the Inertia of a body depend upon its energy content?”.
> >
> > It is proven (IMO) that Einstein NEVER obtained a direct derivation for the
> > formula m=E/c² that appear as a conclusion of the paper. He tried six
> > more times until he gave up in 1942. Yet, the approximation was accepted
> > and generalized for any velocity, even when it's valid for v << c.
> >
> > The circular argument is evident at plain sight, and Planck noticed this
> > by 1906, introducing some corrections to include momentum in 1907.
> >
> > Perhaps, in that epoch, imagining to obtain velocities higher than
> > 30,000 Km/sec (v/c > 0.1) was unthinkable, and E = mc² gained wide acceptance as, by 1910, a CRT with 1,000 V accelerated electrons up
> > o v/c = 0,0625, and only using alpha particles values of c/v = 0.17 were
> > obtained by 1911 in the experiments of Geiger and Marsden. By 1920,
> > Rutherford had obtained alpha particles values of c/v = 0.67, and only
> > by 1930, when proton accelerators were invented, (Van de Graaff,
> > Lawrence, Cockcroft) energies higher than 0.1 MeV (v/c higher than
> > 0.99996) started to be obtained.
> >
> > ----------------- Final part of the 1905 paper -------------------------------------------------
> >
> > Let there be a stationary body in the system (x, y, z), and let its energy—
> > referred to the system (x, y, z) be E₀. Let the energy of the body relative to
> > the system (ξ, η, ζ) moving as above with the velocity v, be H₀.
> > .........
> > If we call the energy of the body AFTER THE EMISSION OF LIGHT E₁ or H₁
> > respectively, measured relatively to the system (x, y, z) or (ξ, η, ζ)
> > respectively, then by employing the relation given above we obtain
> >
> > E₀ = E₁ + 1/2 L + 1/2 L
> >
> > H₀ = H₁ + L/√(1 - v²/c²)
> >
> > By subtraction we obtain from these equations
> >
> > H₀ − E₀ − (H₁ − E₁) = L . (1/√(1 - v²/c²) - 1)
> > ...............
> > Neglecting magnitudes of fourth and higher orders we may place
> >
> > H₀ − E₀ − (H₁ − E₁) = 1/2 L/c² . v²
> >
> > From this equation it directly follows that:—
> >
> > If a body gives off the energy L in the form of radiation, its mass
> > diminishes by L/c2. The fact that the energy withdrawn from the body
> > becomes energy of radiation evidently makes no difference, so that we
> > are led to the more general conclusion that
> >
> > The mass of a body is a measure of its energy-content; if the energy
> > changes by L, the mass changes in the same sense by L/9 × 10²⁰, the
> > energy being measured in ergs, and the mass in grammes.
> >
> > It is not impossible that with bodies whose energy-content is variable
> > to a high degree (e.g. with radium salts) the theory may be successfully
> > put to the test.
> >
> > If the theory corresponds to the facts, radiation conveys inertia between
> > the emitting and absorbing bodies.
> >
> > ----------------- End of the 1905 paper -------------------------------------------------
> >
> > The fallacy of the circular reasoning is two fold:
> >
> > 1) Einstein never introduced the mass M₀, which is at rest in the system
> > (x, y, z). Instead he used its energy content before (E₀) and after (E₁)
> > the light was turned on.
> >
> > 2) He asserted that E₀ = E₁ + L, so (E₀ - E₁) = L is the energy content of M₀
> > which has been converted into light.
> >
> > And due to this assertion, disguised into difference of energy between
> > systems (x, y, z) and (ξ, η, ζ), is that he ASSUME mass M₀ diminishes
> > by L/c².
> >
> > 3) Einstein is tricky enough to NEVER introduce something as M₀.. In the
> > paper always talk about ENERGY, except at the end when a mass loss
> > is asserted as being L/c².
> >
> > The word "mass" appears only 4 times, and in the last paragraphs.
> > The word "inertia" appears only 2 times: in the title and in the last sentence.
> >
> > *******************************************************
> >
> > Using the LAW OF CONSERVATION OF ENERGY (LCE), is easy to prove
> > the fallacies in the paper. It requires the use of Mₒ as the rest mass in
> > the system (x, y, z), for which the LCE applies as follows:
> >
> > (LCE) Kᵢ + Uᵢ = Kₑ + Uₑ , with K and U as kinetic and potential energies.
> >
> > ------------------------------- Excerpts from the paper ------------------------------------
> >
> > Let there be a stationary body in the system (x, y, z), and let its energy—
> > referred to the system (x, y, z) be E₀.
> > .........
> > If we call the energy of the body AFTER THE EMISSION OF LIGHT E₁ or H₁
> > respectively, measured relatively to the system (x, y, z) or (ξ, η, ζ)
> > respectively, then ..................
> >
> > E₀ = E₁ + L
> > H₀ = H₁ + γ . L
> >
> > ------------------------------------ End of excerpts -----------------------------------------
> >
> > Case 1) Applying L.C.E. to system (x, y, z), NOT KNOWING THAT E = mc²
> > is going to be obtained at the end of the paper.
> >
> > M₀ is at rest, so Kᵢ = 0. Also has no potential energy, so Uᵢ = 0.
> > Once the light is turned on, still no variations and Kₑ = Uₑ = 0.
> >
> > The principle of conservation of energy is verified in system (x, y, z)..
> >
> > Kᵢ + Uᵢ = Kₑ + Uₑ
> >
> > Case 2) Applying L.C.E. to system (x, y, z), BUT KNOWING A PRIORI THAT
> > E = mc² is going to be obtained at the end of the paper.
> >
> > M₀ is at rest, so Kᵢ = 0, BUT potential energy in the system (x, y, z)
> > is Uᵢ = Mₒ.c².
> >
> > When the light is turned on, it happens that Kₑ = 0, but the potential
> > energy Uₑ in the system (x, y, z) has changed and is:
> >
> > Uₑ = (Mₒ - L/c²).c² + L
> >
> > In this way, while the mass Mₒ lost an amount equivalent to L/c², the
> > energy in the system (x, y, z) IS CONSERVED, because that loss of mass
> > has been transformed into the energy L of both beams of light.
> >
> > And this is how the circular argument (Petitio Principii) was introduced,
> > disguised under energy and avoiding to talk about mass until the very
> > last words in the paper. It's not MAGIC, it's a FALLACY.
> >
> > I'd like that anyone can analyze this, and prove me wrong with the circular
> > reasoning (begging the question) that the paper has.
> >
> >
> > Now, can anyone to prove me WRONG?
>
>
> "Neglecting magnitudes of fourth and higher orders we may ...".
>
>
> "The fact that the energy withdrawn from the body
> becomes energy of radiation evidently makes no difference, so that we
> are led to the more general conclusion that ...".
>
> The mass of a body is a measure of its energy-content;...".
>
>
> I think you can see that about mc^2, the proportional constant that, according
> to first term Taylor series terms what it's in line with, or what usually work out
> bounds for Fourier and what results things, Einstein left out "here watch me
> drop out otherwise besides the term, here what conserves charge", there is left
> out under potential what is charge then that besides it's a _generous reading_
> and not taking license with Einstein, except to not take license with Einstein.
>
>
>
> What measure there is the speed of light under mass-energy equivalence,
> is a usual drift detector, in a usual general sense always square.
>
> That "the particle accelerator actually does 'shrink', then decompress, on its track",
> is for a usual verifiable experiment that running a particle accelerator in otherwise
> a black box appears to shrink the box.
>
>
> Which I think you might agree GR would also predict it would _look_ like.
>
> (At the time.)