Reconsidered: NEWTON's Cradle and Gravitational Waves, LIGO
Dear Abraham Mjm Einsteig,
dear friends, and dear scientists,
I want to answer Abraham Mjm Einsteig’s question:
Yes, we have considered different explanations, respective interpretations. Amazingly, and knowing about the experimenter’s fallacy, all these alternative explanations we considered fit well, or very well by being complementary, and not exclusive; most of them were discussed at the kitchen table:
1. The power law y=k*t^-0.5 is the realisation of FERMAT’s Extremum Principle related to x,y-trajectories in an EUKLIDIAN space.
2. y=k*t^-0.5 can easily be transformed by *m*g*t into
action = A = k’*t^0.5.
(Karen UHLENBECK stresses the importance of action in her #ABELprize lecture 2019.)
Now, we can see
k’*t^0.5 ~ a(t)
with a(t) being Alexander FRIEDMANN’s scale factor for radiation dominated cosmology. Thus, y=k*t^-0.5 corroborates FRIEDMANN’s extensions of Albert EINSTEIN’s general relativity. Furthermore, our data are compatible with the assumption of some form of radiation in the interaction of the spheres (bosons): HIGGS bosons, phonons, and gravitons.
3. y=k*t^-0.5 is related to NEWTON’s law of gravitation by Tullio REGGE’s trajectories (Leonard SUSSKIND, String Theory and M-Theory, lecture 1, 2010) by angular momentum l~m^2 (m in law of gravitation):
y = Δr= k’’(l^0.5/g)^0.5 = k’’’ t^-0.5;
pendulum length, ꞷ, and 2pi integrated in k’’’.
4. t^-0.5 is the norm of a normal vector, and allows calculating HESSE’s normal vector by “assuming” time is orthogonal to space, and the constant k has a factor, or component being the scalar product of time, and the x,y-space.
Then y is the distance to x according to the HESSE’s distance equation; physically meaning the length of the time vector in the calculations is changing, but the effect of interaction with space not (this is evidence, or a “proof” (see Karl POPPER) for the isotropy of space, see A. FRIEDMANN, and for the conservation of action, respective energy); thus k*t^-0.5 “shows” orthogonality of time, too. Furthermore, thus (i.e. HESSE normalisation) our mathematical model of NEWTON’s cradle is a realisation of David HILBERT’s L^2 space linking the power law y=k*t^-0.5, and our NEWTON’s cradle clearly to quantum mechanics.
5. If you allow negative time you get according to EULER’s identity
y= k*(n*l*t(Planck))*(e^iπ)^-0.5,
and by squaring you get a solution of SCHRÖDINGER’s famous equation (n as factor of periodicity, l*t(Planck) as time quantum to be chosen adequately, and n*l*t(Planck) seen as repetition of the wave with period T=l*t(Planck)):
Amplitude^2 = y^2 = k*[(e^iπ)^-1]^(n*l*t(Planck)) =
Amplitude^2 = y^2 = k*e^(-i*π*n*l*t(Planck)).
Note that time can be seen simultaneously (!) positive as classical mechanics time, and general relativity time, and negative as cyclical quantum wave time with probabilistic impact: no contradiction arises; however many discrepancies in modern physics are solved by allowing two simultaneous forms of time.
6. Squaring of y=k*t^-0.5:
y^2 = k^2/t
is in accordance with my schoolbook definition of quantum physics (PLANCK’s photoelectric effect in EINSTEIN’s interpretation): “The number of exchanged quants every time is proportional to the square of the amplitude of the wave.” (my schoolbook: DORN & BADER: Physik Oberstufe A, 1977, p.16. y is the amplitude of our NEWTON’s cradle oscillator). Thus, our data are compatible with SCHRÖDINGER’s equation, and the basic principles of quantum physics.
7. The power law y=k*t^-0.5 is, looking at points 1. to 6. above, and appreciating the quadrupole argument, and the HERTZ’s contact law argument (2nd derivative), and the δ(NEWTON’s cradle) ≈ π δ(pendulum) graviton existence argument (see earlier) the core equation (SNEED & STEGMÜLLER, structuralistic view of theories) allowing to introduce a theory combining classical mechanics, quantum gravitation, and quantum mechanics etc. . In other words: y=k*t^-0.5 is the equation Albert EINSTEIN was searching, and heading for.
8. … chirps (Yves MEYER) …
9. … … …
I have to care for my family now; I will discuss the arguments above in detail later; I will continue later with point 8., 9., 10. … . Critique is welcome; conjectures and refutations are welcome.
Yours respectfully
Stefan Geier (with help by Caroline Geier, and Stephanie Geier)
Image: Karen UHLENBECK, The ABEL lecture 2019, abelprize.no, official video, 23:55: Oslo, May 22, 2019, courtesy assumed: Glimpses into the Calculus of Variations.
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