johannes

04-18-2010, 01:01 PM

Hello S. Kalimuthu,

here I refer to Spherical Figure 1 of the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf).

You mix up curves and lines.

A curve AB is a continues path between the points A and B.

A line is a special curve that satisfies the condition that if the point P is on the path interval [A,B] then d(A,P) + d(P,B) = d(A,B), where d(X,Y) is the distance between the points X and Y.

This definition of "line" is the general definition of a line in all geometries.

Quote from the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf): Join MA’ , MB’ and MC’. On MA’ , make a point A.

I assume by "join" you mean a line MA', etc.

Quote from the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf): With center M, radius MA, describe an arc cutting MB’ at B and MC’ at C.

The curve AC is NOT NECESSARY a line! This is where your argument goes wrong. A spherical geometry has a maximum length R then only if for the arc d(M,A)=R/2 THEN the curve AC is a line!!!

An arc is a curve, that is only a line for the latitude = 90° for other latidudes the arc is NOT A LINE.

This is why a flight path from cities at the same latidudes above the equator goes slightly to the north pole - as THAT is the shortest distance.

Here is an example from chicago (in USA) to delhi (in India) Flightpath from Chicago to Delhi (http://www.divisionloop.com/images/casualfridaysuniversal_77C9/FlightPath.jpg)

You argument is correct for curves but NOT FOR LINES!

Regards - Johannes

here I refer to Spherical Figure 1 of the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf).

You mix up curves and lines.

A curve AB is a continues path between the points A and B.

A line is a special curve that satisfies the condition that if the point P is on the path interval [A,B] then d(A,P) + d(P,B) = d(A,B), where d(X,Y) is the distance between the points X and Y.

This definition of "line" is the general definition of a line in all geometries.

Quote from the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf): Join MA’ , MB’ and MC’. On MA’ , make a point A.

I assume by "join" you mean a line MA', etc.

Quote from the document No Quantum Gravity (http://www.mrelativity.net/Papers/40/TOE.pdf): With center M, radius MA, describe an arc cutting MB’ at B and MC’ at C.

The curve AC is NOT NECESSARY a line! This is where your argument goes wrong. A spherical geometry has a maximum length R then only if for the arc d(M,A)=R/2 THEN the curve AC is a line!!!

An arc is a curve, that is only a line for the latitude = 90° for other latidudes the arc is NOT A LINE.

This is why a flight path from cities at the same latidudes above the equator goes slightly to the north pole - as THAT is the shortest distance.

Here is an example from chicago (in USA) to delhi (in India) Flightpath from Chicago to Delhi (http://www.divisionloop.com/images/casualfridaysuniversal_77C9/FlightPath.jpg)

You argument is correct for curves but NOT FOR LINES!

Regards - Johannes