# Thread: Rods and contacts, Poles and barns.

1. Originally Posted by Hetman
r_1 + r_2 = 2a; r_1 = c_1t; r_2 = c_2t; a = ct;

In the context of experiments designed to measure the speed of light, that is ellipsoid, and only the ellipsoid.

Poincare's ellipsoid, from which we get Einstein's sphere, after applying the Lorentz transformation.
the equation you wrote down c1 + c2 = 2a was the equation of an average or the equation for a straight line when c1 and c2 are ordinates, and that's that, any ellipse will have the ordinates squared.

now you change to r1 and r2 for some reason, which probably is, that you suddenly want to change to polar coordinates, where, if I am not mistaken there is defined:

which would be an ellipse, however, does not have anything to do with "measuring the average speed in a two-way experiment."

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Originally Posted by tusenfem
the equation you wrote down c1 + c2 = 2a was the equation of an average or the equation for a straight line when c1 and c2 are ordinates, and that's that, any ellipse will have the ordinates squared.

now you change to r1 and r2 for some reason, which probably is, that you suddenly want to change to polar coordinates, where, if I am not mistaken there is defined:
Exactly.

But there is no coordinates, but only the relationship that defines the ellipse.

Then we can introduce arbitrary coordinates and calculate the equation of this ellipse.

Originally Posted by tusenfem

which would be an ellipse, however, does not have anything to do with "measuring the average speed in a two-way experiment."
For over a hundred years, only this dependence is determined, and the people performing the experiments are probably unaware of this fact, as evidenced by your reaction.

Effectively / visually we have a sphere: two-way communication requires the same amount of time for any direction, so the points of the ellipsoid are equidistant in the case of any pair of stationary receiver / transmitters; it's sphere from a practical point of view.

Propagation of waves from a moving source:

http://home.scarlet.be/leo.gooris/mich/page9.html
Last edited by Hetman; 2012-Jun-25 at 02:10 PM.

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Originally Posted by Hetman
But there is no coordinates, but only the relationship that defines the ellipse.
Why no coordinates?
The vision that was pivotal to my thinking about the pole and barn type experiments is that we can think of both reference frames as one Minkowsky coordinate system superimposed on another. Pick either one as inertially at rest and motion then rotates the second system about the y axis through a fourth dimension of space. The greater the velocity, the greater the rotation and complete 90 degree rotation would represent conditions at what many refer to as “the speed of light.” This rotation shortens the apparent length of objects in the moving reference frame just as the shadow of a rod can be made to appear longer or shorter by rotating it in the light. A pole at rest can span the distance from A to B simultaneously in our reference frame and from A' to B' in the other but A' to B' appears shorter relative to our A to B at rest. We see the moving pole travel from A to B in our reference frame where it connects to both one at a time by virtue of its motion but we don't see that the connection is simultaneous in the moving reference frame. The connection is simultaneous in the moving frame but we can't observe it as simultaneous in ours because it lies on a different spacetime axis.
Now, if we connect the dots (tips of the poles) A to B on one axis with the relatively shorter A' to B' on the rotated axis, they would all lie on the perimeter of an ellipse that connects two Minkowsky coordinates and would that be the ellipse you are discussing?

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Originally Posted by Bob Angstrom
Why no coordinates?
The vision that was pivotal to my thinking about the pole and barn type experiments is that we can think of both reference frames as one Minkowsky coordinate system superimposed on another. Pick either one as inertially at rest and motion then rotates the second system about the y axis through a fourth dimension of space. The greater the velocity, the greater the rotation and complete 90 degree rotation would represent conditions at what many refer to as “the speed of light.” This rotation shortens the apparent length of objects in the moving reference frame just as the shadow of a rod can be made to appear longer or shorter by rotating it in the light. A pole at rest can span the distance from A to B simultaneously in our reference frame and from A' to B' in the other but A' to B' appears shorter relative to our A to B at rest. We see the moving pole travel from A to B in our reference frame where it connects to both one at a time by virtue of its motion but we don't see that the connection is simultaneous in the moving reference frame. The connection is simultaneous in the moving frame but we can't observe it as simultaneous in ours because it lies on a different spacetime axis.
Now, if we connect the dots (tips of the poles) A to B on one axis with the relatively shorter A' to B' on the rotated axis, they would all lie on the perimeter of an ellipse that connects two Minkowsky coordinates and would that be the ellipse you are discussing?
But what's the problem?
Effectively there is always a sphere, which is equivalent to Einstein's postulate: c = const.
It is full agreement with the experiments - but thanks to the ellipsoidal wavefront, and not a contraction!

Contraction occurs only in Minkowski space, which we get after applying the Lorentz transformation, and not before. Here one can analyze these various paradoxes, but probably only in the context of entertainment, or art (though these paradoxes are the result of mixing two incompatible concepts of space).

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