gordonjudd wrote: ↑
Thu Jun 20, 2019 2:19 pm
Even Newton knew that the results you get in a moving frame that is moving at a constant velocity and direction (thus an inertial frame of reference
) should match the results you get in an earth frame so I don't know why you seem to think a moving frame should not be used to analyze loop propagation.
Because the loop has no inertia of its own. Only the elements of line within it have mass and velocity.
Let's look at something that can be easily analysed with a moving frame of reference: the valve
on the front wheel of Paul's triathlon bike. If someone were to track its path along the road in an Earth frame of reference, it would describe a cycloid.
That looks pretty nasty. Trying to analyse the physics of the valve's motion from that would be quite difficult.
However, from Paul's point of view on the bike (since he occupies the moving frame of reference), the valve is traveling in a circle around the axel. He can look down and see it going around and around, over and over. The moving FoR is valid here because the wheel on which the valve sits is a solid object, with both mass and velocity (hence inertia) and the separate parts of the wheel do not change their position relative to each other.
That is, they maintain a consistent spatial relationship
with each other.
The physics of the valve's motion are fairly easy to analyse from Paul's point of view. It's just 5 grams of metal traveling in a circle around the axle. That's the power of a moving FoR.
When Paul crashes into an Asian Elephant on his training ride (because he's watching the valve on his front wheel), the bike stops moving, wheel stops moving and the valve stops moving. The elephant cannot stop the valve alone and let Paul ride on by. Stopping any part of the wheel stops the whole wheel. A moving FoR is valid here because the hub, spokes, rim, tyre and valve can be considered as a single mass.
The physics of the fly line in motion can't be analysed in the same way. Stopping the loop has no impact on the line in the fly leg. It keeps moving forward. Casting at an Asian Elephant doesn't mean the fly drops as soon as the loop hits the beast. The fly leg has inertia and it keeps piling into the elephant with no loop in sight.
A moving FoR focusing on the loop is not valid because mass is always moving in and out of the object (loop). In physics terms, it's no more a single object than a flock of birds is. Shooting one bird in the flock does not stop the flock from flying past: the bird does not maintain a fixed spatial relationship with those around it. In the same way, stopping a single marker on a fly line does not stop the others behind it from continuing on their path.
Tracking a single point on the line shows that it never follows the form of a loop. To draw it any other way is misleading.