Need help understanding this math

[Didymus]

I'll try rephrasing my question, as I do not wish to question the theory itself. Verily, verily, it would be unconscionable for me... in a place like this... to go about questioning theories. So, I'll clarify the below questions as an attempt to understand the math behind that theory. Verily, verily, special relativity is uniformly accepted... however... with my wicked, finite mind, I am not strong enough to understand the very experiment that provide's it's proof. Surely the end is is without question... but I need... help. I need help understanding the supporting math.

Happy?

1- Preface: The math I've seen states that the altitude of the plane was negligible in the equation... but... normal cruising altitude for jets capable of intercontinental flight is about 30,000 feet... this would add about .1% to the radius and therefore a quite measurable velocity change relative to the imaginary Earth core. This much was negligable, yet, the measurements they took yielded a change over a 3 day flight of 50 nanoseconds... 50 billionths of a second over 72 hours of flight seems like the results could easily be skewed by discounting a .1% change in the formula.

Question: Does anyone know if they actually did take into account the average altitude of the aircraft? If not, can someone give a logical explanation as to why we accept results that are orders of magnitude smaller than what the math says is a negligible amount?

2- the numbers I was able to find:

Predicted: Time difference in ns
Eastward Westward
Gravitational 144 +/- 14 179 +/- 18
Kinematic -184 +/- 18 96 +/- 10
Net effect -40 +/- 23 275 +/- 21
Observed: -59 +/- 10 273 +/- 21
The problem encountered with measuring the difference between a surface clock and one on an aircraft is that neither location is really an inertial frame. If we take the center of the Earth as an approximation to an inertial frame, then we can compute the difference between a surface clock and the aircraft clock. Taking a "proper time" at the Earth's center as if the master clock were there, the time measured by a clock on the surface would be larger

preface: In what way is this not circular reasoning? The clocks on the aircraft and the earth, taken directly, obviously didn't work out to their calculations. Therefore they went out to prove math that suggests that the two clocks would be different by a very small amount... and adjusted BOTH the test clocks and their control clocks by that math. Of course the experiment functioned as predicted because the control was adjusted by their predicted math!

Question: Is the above source just grossly inaccurate? Is there a more reliable source somewhere that takes numbers directly from some space? If not... how does anyone accept this as evidence for anything?... of course the theory itself is water tight. Special Relativity is the one true theory, regardless of any failures of imperfect men testing it.

 

[Bill_K]

Does anyone know if they actually did take into account the average altitude of the aircraft?

Of course they took it into account! These are top-notch scientists, not amateurs. In fact the effect due to the difference in altitude was one of their two main results.

In what way is this not circular reasoning? The clocks on the aircraft and the earth, taken directly, obviously didn't work out to their calculations.

No, the point is that SR and GR affect both clocks, so they calculated the difference, and their measurements agreed with the calculation.

 

[Didymus]

k... was hoping for a bit more than "they took it into account." Is there any record of what formula they used... beyond what's found here: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html#c3

... because according to that math, they assumed the jets flew at sea level...

 

[Bill_K]

Have you read the Wikipedia page? Plus the numerous other references given there.

 

[Didymus]

k... where in there do you see the altitude of the plane accounted for?