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dseppala

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This is the barn pole paradox using a slightly curved pole and a silo instead of a perfectly straight pole and doors on a barn. Let's say we have a pole of proper length of 1 light-year that is traveling around a circle that has a curvature of 1 meter over 1 light-year of length. Let that pole rotate around the circumference of a circle with each point of the pole having an angular velocity of V = 0.866c.

From the point of view of the rest frame of the circle, this rotating pole's length when it is virtually parallel to the x-axis is 0.5 light-years in length (due to length contraction), with a curvature of slightly less than 1 meter over this 0.5 light-year length. We then build two cylinders with centers at the center of this circle, one with a diameter slightly larger than the circle the rotating pole is traveling around and one with a diameter slightly smaller than the circle the rotating pole is traveling around. These two cylinders now encase the rotating pole as it travels along the circumference of a very large circle. Since these cylinders are in the rest frame of the circle, we build the larger one with a diameter that has a curvature slightly larger than 1 meter over a 0.5 light-year length (just slightly larger than the pole's curvature) and the inner cylinder with a slightly smaller diameter. The rotating curved pole just fits in the space between these two cylinders as it rotates around the circle.

Now we look at another inertial reference frame that is moving with V = 0.866c relative to the rest frame of the circle and cylinders. When the pole is moving in that same direction as this moving reference frame they have virtually zero relative velocity. This moving frame measures the length of the pole to be just slightly less than 1 light-year in length with a curvature of slightly less than 1 meter over that 1 light-year of length. This same moving frame measures the curvature of the two cylinders to have about 1 meter of curvature over 0.25 light-years of length (due to length contraction) over the arc length where the moving pole is at this point in time.

How does the moving frame explain how this slightly curved pole fits into the space between the two cylinders that have four times the curvature?

Thanks,

David Seppala

Bastrop TX

From the point of view of the rest frame of the circle, this rotating pole's length when it is virtually parallel to the x-axis is 0.5 light-years in length (due to length contraction), with a curvature of slightly less than 1 meter over this 0.5 light-year length. We then build two cylinders with centers at the center of this circle, one with a diameter slightly larger than the circle the rotating pole is traveling around and one with a diameter slightly smaller than the circle the rotating pole is traveling around. These two cylinders now encase the rotating pole as it travels along the circumference of a very large circle. Since these cylinders are in the rest frame of the circle, we build the larger one with a diameter that has a curvature slightly larger than 1 meter over a 0.5 light-year length (just slightly larger than the pole's curvature) and the inner cylinder with a slightly smaller diameter. The rotating curved pole just fits in the space between these two cylinders as it rotates around the circle.

Now we look at another inertial reference frame that is moving with V = 0.866c relative to the rest frame of the circle and cylinders. When the pole is moving in that same direction as this moving reference frame they have virtually zero relative velocity. This moving frame measures the length of the pole to be just slightly less than 1 light-year in length with a curvature of slightly less than 1 meter over that 1 light-year of length. This same moving frame measures the curvature of the two cylinders to have about 1 meter of curvature over 0.25 light-years of length (due to length contraction) over the arc length where the moving pole is at this point in time.

How does the moving frame explain how this slightly curved pole fits into the space between the two cylinders that have four times the curvature?

Thanks,

David Seppala

Bastrop TX

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