IF its fair game for round earth science to bend space and time itself, why is it all of a sudden ridiculous when a flat earther does it? Psh.
No-one claims that "round earth science" bends "space and time". Einstein's GR claims that "space-time" is curved!
This seems silly to me - "no one claims x, Mr. Y claims x. Space-time being curved also means space is being curved. Just look at gravitational lensing to see this.
And if you are able to do the calculations (I won't pretend to), it can be shown that in the Solar System the "space" component is only bent a miniscule amount.
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An orbiting satellite could be rotating in a perfect circle in space, but in space-time it is following a geodesic, in other words the shortest distance between its location in space-time now and sometime in the future. This is more or less akin to the shortest distance between two points on the globe not being a "straight line" (that is not possible), but a "great circle" or geodesic.
So yes, Space-time is curved, leading to what we call gravity, but not nearly enough to make a plane surface seem like a sphere!
Of course you are free to pursue what hypotheses you like, but even Einstein's work did not "simply come out of thin air".
This grew like Topsy, but maybe if I keep at it long enough I might finally understand it anyway, I don't know anout anyone else!
Ignoring GR and SR, if we already know euclidean physics is incorrect. Therefore its more than reasonable for me to look at non-euclidean solutions for maps.
What I was trying to get over is that
if you accept Einstein's GR then in our part of space away from massive objects, such as black holes,
then there almost no curvature of space. Yes, space is curved, but by an almost immeasurable amount.
Now, maybe the "Ferrari effect" might allow the
John Davis GR to postulate curvature sufficient to make a
Flat Earth appear spherical, but please
do not pretend that Einstein's GR justifies your doing that.
What you are talking about is a
whole different hypothesis that you must provide evidence for. Otherwise it is just a
Davis hypothesis. Fine, you are free to do that, but until your version is accepted you can hardly base arguments on it. You may set yourself up as correcting Newton and Einstein. Fine, that's up to you, but please don't expect us to accept that without some good evidence.
Then you claim "Ignoring GR and SR, if we already know euclidean physics is incorrect. Therefore its more than reasonable for me to look at non-euclidean solutions for maps." But, where have you proved that
"euclidean physics is incorrect"?
As far as I am concerned the earth (and our immediate neighbourhood in space - away from the likes of black holes) is essentially
3-D Euclidean space. I say essentially, because there is very slight and calculable (not by me I freely admit) curvature of space, and more easily measurably of time (fast moving, or extremely high altitude clocks run at different rates).
Now if ones movement is constrained to the
surface of a sphere (and the Earth's surface
approximates that) we can say that we are in a non-Euclidean space. But, of course in fact we are
not constrained to the Earth's surface - we could, at least i
n principle take the true straight line distance between two points on the Earth's surface (though at present impossible in practice) and we can and do fly well above the Earth's surface.
The apparent non-Euclidean nature shows up when we try to find the shortest distance along the surface from point A to point B, then the Great Circle (a geodesic in our non-Euclidean 2-D space) gives
an excellent approximation to the distance - only an approximation because the earth is not a perfect sphere. You will find that different sources give slightly different distances between the same two points - the value depends of the earth shape used in the calculation - sphere, oblate spheroid or better.
The non-Euclidean nature again shows up in measuring the sum of angles for say a triangle constrained to the surface of a sphere. We get a spherical excess of
720° x (area of triangle) /(area of sphere)
.
Now, before some keen person sets off to prove the earth a sphere that way, just look at the accuracy you would need! Yes, Geodetic Surveyors regularly meet this, but on any but massive triangles this extra angle is very small.
Yes, John of course it's OK for you "to look at non-euclidean solutions for maps", but please don't justify this from Einstein's theories, make sure you base it on your own as yet unproved hypotheses, and don't claim that "
we already know euclidean physics is incorrect." It is more accurate to say that
John Davis believes that "euclidean physics is incorrect."