The Pioneer anomaly

[modest]

Originally Posted by Viv Pope

tR = √(s2 + t2) Pythagoras
This Pythagorean time-equation and the customary Einsteinian one, are inter-transformable. For instance, if it were necessary to express this same time-resultant, tR, in Einsteinian terms, then, since the relative velocity of the motion is the distance s travelled in the time tR (i.e., v = s/tR ), all we have to do is to substitute for s, in the Pythagorean equation, the equivalent vtR and then simplify, which produces the familiar (to physicists) equation:
tR = t/√√(1 – v2/c2). Einstein

This does work. If we observe someone from earth who is in a rocket. They are traveling half a light-year per year from our perspective then after five of our earth years...

By the lorentz transformations their clock has advanced 4.33 years as we observe it. They have traveled 2.5 light-years as we see it. We therefore have observed them:



It's basically the inverse of a normal Lorentz transformation rearranged a bit (you have to multiply time by velocity to get distance in light-distance) I'll show the math if anybody asks. I don't think this is significant except to say:

The Lorenz transformations can be derived from "Pythagorean" geometry. The constraints are that all axes are at right angles and light as a vector must follow the Pythagorean relationship to two of those axes. That is the consistent thing that makes the transformation possible. None of this was beyond Einstein. Nor do I think you can call it "relativity without Einstein" as the relationship relies on the consistent speed of light.

~modest

EDIT:
I will show the math as it's incredibly easier than I was picturing in my head:
Normal Transformation:

Multiply T' by the binomial and square:

So, yeah, not too much past Einstein's abilities I'd wager

Second edit: (I seem to have lost the ability to do basic algebra):

Starting with the more accurate transformation:

squaring both sides:

Rearrange:

Multiply by the binomial and rearange:

and you get:

Ok, I think that's right.

[Viv Pope]

Originally Posted by CraigD

In order to confirm that I understand the point Viv intended to make with these statements, let me restate my read of it:
“The concept of the speed of light in vacuum (c) is logically incoherent, because the speed of light cannot be measured in a system consisting only of light in vacuum.”

However, I’ve not previously encountered a definition of the c as “the speed of light measured with only vacuum”, and am practically certain this is not the definition intended to be used in the Second Postulate of Special Relativity:

The Principle of Invariant Light Speed - Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source.

(source: wikipedia article “special relativity”)

The usual definition of the speed of light in any medium is the same as that of the average speed of anything: , where and are changes in distance and time. Although direct measurement of for practical values of were experimentally impractical 100 years ago, they are no longer (eg: see “A small tabletop experiment for a direct measurement of the speed of light”, Aoki and Mitsui, 2008).

Although, to a person subscribing to a corpuscular theory of light (eg: Isaac Newton and many other 18th century natural philosophers), the idea that a direct measurement of the speed of light results in a constant value regardless of the motion of the emitter or receiver of the light is counterintuitive and unexpected, such results are reproduced literally many times a second worldwide, in particular by the GPS. The precision of the clocks and signal shapes of the GPS and other systems performing long-distance speed of light measurements is sufficient that a violations of the second postulate would be easily detected. No such violations are detected.

Therefore, rather than being nonsensical, as Viv claims, the second postulate seems to me superbly supported by experiments.

Viv, do I appear to understand your claims? If not, how have I erred?

If so, what is your experimental evidence for violations of the second postulate, or explanation for why violations are not experimentally detectable?

[Viv Pope replies

Dear Craig D,
As you will surely know, physics doesn't advance entirely by adding more and more 'experimental evidence' in a continuous series.Some of the biggest. most revlutionary advances are made by different interpretations of the same evidence. A famous example of this was supplied by Copernicus. Before he came on the scene it was 'evident' that the sun. moon and planets orbited the earth. Copernicus offered no experimental 'evidence' for his revolutionary shift in thinking towards seeing our earth and the other planets orbiting the sun, yet it turned out, in the end analysis. that this latter interpretation of the 'evidence' was far more acceptable than the former

This is the sort of conceptual 'flipover' that I have offered to this group for serious and intelligent consideration. In philosophy of physics, these different interpretations of physical evidence are judged by the criterion of conceptual economy called 'Ockham's Razor', whose use is to shave off logically unnecessary, or redundant, assumptions. It is this 'Ockham's Razor' that I have applied to Einstein's Second Axiom, showing that both it and its entourage of conceptual puzzles can be removed without affecting the practical consequences of Relativity in the least. In the equations, the value and dimensions of c are the exactly same, whether c is interpreted as a 'velocity' or a pure dimensional constant, in the way Herman Bondi and I have concurred. Both he and I have agreed that Relativity is much simpler to understand and to teach without c being interpreted n Einstein's way as a 'velocity'. You may see this if you search for POAMS on Google.

I hope that helps.

Viv Pope