hyksos wrote:This is where I'm gonna have to cut you off.

I always stop for school buses.

hyksos wrote:Some caveats and qualifications and clarifications are needed.

We don't really need an additional interpretation of the stopwatch hands of Feynman, because we already know what they are.

Feynman used the word "arrows" he was actually referring to what are called Probability Amplitudes…

Yes, quite! But Feynman doesn't know what

'probability amplitudes' are. So far, I'm the only one who does.

The Character of Physical Law"…we invent an 'a' which we call a probability amplitude, because we do not know what it means." p.137

"Nobody knows any machinery. Nobody can give you a deeper explanation…no one can go any deeper today… there is probability all the way back…in the fundamental laws of physics there are odds. " p145

"Nobody knows how it can be like that." p.129

"Probability amplitudes are very strange…" p.166

L. Susskind, A. Friedman

Quantum Mechanics; Theoretical Minimum"These [probability amplitudes] are extremely abstract, and it is not at all obvious what their physical significance is. " p.38

Wikipedia"It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics - topics that continue to be debated even today. "hyksos wrote:When Feynman said "add up all the arrows" he was actually performing integration. … the Path Integral in textbooks.

He sums arrows as with vector addition, and some rules for reversing arrows (e.g. reflections).

hyksos wrote:You need not chase down and identify the "what object is spinning". We already know what it is. The clock hands on a stopwatch Feynman keeps talking about are actually parts of the Schrödinger Wave.

Again, physics doesn't yet know what the

Schrödinger wave is

physically. I supply this.

hyksos wrote:They are not real-valued vectors. They are complex numbers (complex vectors) in a Hilbert space.

You're making my point.

Physics isn't physics unless its about the physical. Otherwise we're just

math-turbating. Hilbert space isn't worth a hill of beans, if it does not have a

physical basis. It was invented because those poor souls failed to arrive at Euclidean, interval-time coordinates. Complex coordinates can apply there but it's simpler to consider 2D slices to explain many concepts.

hyksos wrote: The frequency at which this clock hand rotates is directly proportional to the momentum of the particle. λ = h/p = h/mv

That's fine. I don't find that inconsistent with

E = hf, where

f = ω_{}3/4pi, the frequency of chronaxial spin. Spatial spin projections reflect that frequency. Recall Feynman's mass-energy declaration:

"Because the muon has a mass about 200 times higher than the electron, the ‘stopwatch hand’ for a muon turns 200 times more rapidly than that of an electron." -

QED, p.143

hyksos wrote:Photons have no mass, and always travel at c…

In addition to what Bangstrom wrote, recall that photons are superfluous. Light quanta typically correspond to the energy difference of orbital transition. After emission, the electron associated with the transition will have a lower chronaxial spin rate (i.e. frequency).

My point, in this thread, is to assert

all energy is fundamentally chronaxial spin rate.hyksos wrote:Faradavian pinholes are objects in our regular 3D space, even when they are drawn outside the lightcone.

I need to clarify.

Pinholes are real, lightlike objects, replacing photons. Pinholes are available at all spatial locations and in every spatial direction but only at universal speed limit

c (thus limited to energy and information). That's the same as saying a pinhole makes a lightlike angle with time in 4D (pinholes are

c-dependent). Massive particles make contact through pinholes. Particles are in fact, pinholes with chronaxial spin. That's the fundamental mass-energy link.

Similarly,

probability amplitude is a

physically real intermediary. It happens to be immeasurable because to do so destroys its status as an

intermediary. I provide the example of spin correlation to explain what Max Born never knew about his rule.

"There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. ... probability is equal to the amplitude-squared" Wikipedia"How does it [the Born rule] work? What is the machinery behind the law?...No one can explain…We have no ideas about a more basic mechanism from which these results can be deduced." Six Easy Pieces pp.134-5

With 100%the probability of self correlation, probability amplitude (a) is the spin projection on the angle bisector between prepared and subsequently measured spin components. Thus, it cannot be both measured and the angle bisector. Nevertheless, it is physically real. Probability (P) that the sign of the subsequently measured component will correlate is in turn the projection of the amplitude on the measured axis. Thus, the Born rule is born.