In this thread I simplified a previous posting about a Knotty problem.

This thread uses the images found here:
https://www.flickr.com/photos/193222248@N05/51250085660

Figure 1 shows two parallel wires. One end of one wire is connected to the top of Plate A and the other end of that wire is connected to the top of Plate B. The other wire has one end connected to the bottom of Plate A and the other end of that wire is connect to the bottom of Plate B. These two wires are always connected to the two plates.

Figure 2 shows how the wires appear if one plate is rotated (in the y-z plane) one revolution and the other plate is not rotated.

Without rotating either plate or without disconnecting either of the wires, it is impossible to make the wires shown in Figure 1 to overlap each other as shown in Figure 2. The two wires only overlap as shown in Figure 2 if one of the plates has rotated one revolution more than the other.

The question I have is if there are two inertial reference frames, F0 and F1, with relative velocity V and the length of the wires is L, and the wires are initially shown as in Figure 1, if frame F1 starts each plate rotating simultaneously at the same rate, and with V and L, frame F0 observers measure that Plate A made one revolution before Plate B starts rotating, how does frame F1 explain how the wires became overlapped at a point in time as shown in Figure 2?

Thanks,
David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 9:32:17 AM UTC-7, sep...@yahoo.com wrote:
> In this thread I simplified a previous posting about a Knotty problem.

Your fully-specified scenario in the previous threads was thoroughly answered and explained, multiple times, but you forgot to acknowledge this before running away. Don't you have something you need to say? (Hint: You're welcome.)

> The wires are initially shown as in Figure 1, if frame F1 starts each plate rotating
> simultaneously at the same rate, and with V and L, frame F0 observers measure that
> Plate A made one revolution before Plate B starts rotating, how does frame F1 explain
> how the wires became overlapped at a point in time as shown in Figure 2?

You have not specified how the parts of the wires are compelled to move, you have only specified how the end points move. If, for example, you force the wires to remain straight and parallel to the axis in terms of F1, then the wires will be helical in terms of F0, and hence will not contact each other. On the other hand, if you force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then in terms of F1 the wires acquire a decreasing helical path making -1/2 turn down to the axis, where they twist +1 times around, and then an increasing helical path making -1/2 turn back to the connection points, for a net of 0 turns.

Of course, there are infinitely many other shapes you could force the wires to take, and translating the descriptions from one system of coordinates to another is just as trivial as i the two cases described above. As always, you simply need to specify what happens in your scenario, and then that's what happens, and you can describe it in terms of any system of coordinates you like. Understand?

On Tuesday, June 15, 2021 at 12:51:25 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 9:32:17 AM UTC-7, sep...@yahoo.com wrote:
> > In this thread I simplified a previous posting about a Knotty problem.
> Your fully-specified scenario in the previous threads was thoroughly answered and explained, multiple times, but you forgot to acknowledge this before running away. Don't you have something you need to say? (Hint: You're welcome.)
>
> > The wires are initially shown as in Figure 1, if frame F1 starts each plate rotating
> > simultaneously at the same rate, and with V and L, frame F0 observers measure that
> > Plate A made one revolution before Plate B starts rotating, how does frame F1 explain
> > how the wires became overlapped at a point in time as shown in Figure 2?
> You have not specified how the parts of the wires are compelled to move, you have only specified how the end points move. If, for example, you force the wires to remain straight and parallel to the axis in terms of F1, then the wires will be helical in terms of F0, and hence will not contact each other. On the other hand, if you force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then in terms of F1 the wires acquire a decreasing helical path making -1/2 turn down to the axis, where they twist +1 times around, and then an increasing helical path making -1/2 turn back to the connection points, for a net of 0 turns.
>
> Of course, there are infinitely many other shapes you could force the wires to take, and translating the descriptions from one system of coordinates to another is just as trivial as i the two cases described above. As always, you simply need to specify what happens in your scenario, and then that's what happens, and you can describe it in terms of any system of coordinates you like. Understand?

When you say,
"if you force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then in terms of F1 the wires acquire a decreasing helical path making -1/2 turn down to the axis, where they twist +1 times around, and then an increasing helical path making -1/2 turn back to the connection points, for a net of 0 turns".

Whenever I try to do something like that with two strings that start out parallel, the two strings always intersect at two points between A and B. I cannot make them only overlap at one point between A and B like they are shown in Figure 2.

David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 12:11:37 PM UTC-7, sep...@yahoo.com wrote:
> > > The wires are initially shown as in Figure 1, if frame F1 starts each plate rotating
> > > simultaneously at the same rate, and with V and L, frame F0 observers measure that
> > > Plate A made one revolution before Plate B starts rotating, how does frame F1 explain
> > > how the wires became overlapped at a point in time as shown in Figure 2?
> >
> > You haven't specified how the parts of the wires are compelled to move, you have only specified how the end points move. If, for example, you force the wires to remain straight and parallel to the axis in terms of F1, then the wires will be helical in terms of F0, and hence will not contact each other. On the other hand, if you force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then in terms of F1 the wires acquire a decreasing helical path making -1/2 turn down to the axis, where they twist +1 times around, and then an increasing helical path making -1/2 turn back to the connection points, for a net of 0 turns.
>
> Whenever I try to do something like that with two strings that start out parallel, the two strings always intersect at two points between A and B.

So, now you're proposing yet another shape, saying that you somehow make the strings converge from one disk down to a point of contact on the axis, then diverge away from the axis, then converge again to a second point of contact on the axis, and then diverge again to the other disk. That's a very bizarre shape to force the strings to take, but if that's the shape you want them to have -- and you have enough hands to make it happen -- then so be it. As I said, you can force the strings to take any shape you like. Describing any arbitrary shape in terms of the different systems of coordinates is just as trivial as it is for the first two shapes that you described. Needless to say, the number of distinct points of contact is invariant. Understand?

On Tuesday, June 15, 2021 at 2:54:48 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 12:11:37 PM UTC-7, sep...@yahoo.com wrote:
> > > > The wires are initially shown as in Figure 1, if frame F1 starts each plate rotating
> > > > simultaneously at the same rate, and with V and L, frame F0 observers measure that
> > > > Plate A made one revolution before Plate B starts rotating, how does frame F1 explain
> > > > how the wires became overlapped at a point in time as shown in Figure 2?
> > >
> > > You haven't specified how the parts of the wires are compelled to move, you have only specified how the end points move. If, for example, you force the wires to remain straight and parallel to the axis in terms of F1, then the wires will be helical in terms of F0, and hence will not contact each other. On the other hand, if you force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then in terms of F1 the wires acquire a decreasing helical path making -1/2 turn down to the axis, where they twist +1 times around, and then an increasing helical path making -1/2 turn back to the connection points, for a net of 0 turns.
> >
> > Whenever I try to do something like that with two strings that start out parallel, the two strings always intersect at two points between A and B.
> So, now you're proposing yet another shape, saying that you somehow make the strings converge from one disk down to a point of contact on the axis, then diverge away from the axis, then converge again to a second point of contact on the axis, and then diverge again to the other disk. That's a very bizarre shape to force the strings to take, but if that's the shape you want them to have -- and you have enough hands to make it happen -- then so be it. As I said, you can force the strings to take any shape you like. Describing any arbitrary shape in terms of the different systems of coordinates is just as trivial as it is for the first two shapes that you described. Needless to say, the number of distinct points of contact is invariant. Understand?

No, I am not proposing another shape. If I force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist around each other and then ramp back linearly up to the contact points, then it is impossible for me to make that happen unless one plate makes one complete rotation if the wires start out parallel. If I do not rotate one of the plates, then it is impossible for me to make the wires (or strings) overlap at only one point. So in any scenario where the two plates have no rotation relative to each other then it is impossible for me to have the two wires overlap at only one point between A and B.

David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 1:19:28 PM UTC-7, sep...@yahoo.com wrote:
> No, I am not proposing another shape.

Yes you are. First you proposed a shape with no points of contact, then you proposed a shape with one point of contact, and then you proposed a shape with two points of contact. Those are three different shapes, because the number of points of contact is invariant.

> If I force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist
> around each other and then ramp back linearly up to the contact points...

That's your second shape, mentioned above.

> then it is impossible for me to make that happen unless one plate makes one complete
> rotation if the wires start out parallel.

In terms of F0 one plate begins to rotate and completes one rotation before the other plate begins to rotate, so thereafter in terms of F0 there is one net turn of the wires between the plates at any given time of F0, whereas in terms of F1 there is 0 net turns of the wires between the plates at any given time of F1. Are you honestly unable to grasp this?

Note also that the number of points of contact is distinct from the number of net turns.

> If I do not rotate one of the plates...

In terms of F0 you begin rotating one plate after the first plate has completed one rotation, so at a given time of F0 there is one rotation difference between their orientations.

> then it is impossible for me to make the wires (or strings) overlap at only one point.

Again, the number of points of contact is distinct from the number of spatial turns at a given time slice of a given frame. You are totally confused about multiple elementary things. You just need to think more clearly and pay attention to the patient explanation that has been provided to you.

> So in any scenario where the two plates have no rotation relative to each other...

Wait, you yourself said you begin the plate rotations simultaneously in terms of F1, so they do not begin simultaneously in terms of F0, and so you cannot say they have "no rotation relative to each other" during the period of time of F0 when one is rotating and the other is not. This is how the one turn in the wires is introduced. Understand? (It's so strange than you are having trouble understanding this now, because you seemed to understand it in your previous scenario when the wire was attached to the rotating cylinder, and 10 turns were introduced in terms of F0. Remember?)

On Tuesday, June 15, 2021 at 4:14:46 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 1:19:28 PM UTC-7, sep...@yahoo.com wrote:
> > No, I am not proposing another shape.
> Yes you are. First you proposed a shape with no points of contact, then you proposed a shape with one point of contact, and then you proposed a shape with two points of contact. Those are three different shapes, because the number of points of contact is invariant.
> > If I force the parts of the wires in terms of F0 to ramp down linearly to the axis and twist
> > around each other and then ramp back linearly up to the contact points....
>
> That's your second shape, mentioned above.
> > then it is impossible for me to make that happen unless one plate makes one complete
> > rotation if the wires start out parallel.
> In terms of F0 one plate begins to rotate and completes one rotation before the other plate begins to rotate, so thereafter in terms of F0 there is one net turn of the wires between the plates at any given time of F0, whereas in terms of F1 there is 0 net turns of the wires between the plates at any given time of F1. Are you honestly unable to grasp this?
>
> Note also that the number of points of contact is distinct from the number of net turns.
>
> > If I do not rotate one of the plates...
>
> In terms of F0 you begin rotating one plate after the first plate has completed one rotation, so at a given time of F0 there is one rotation difference between their orientations.
> > then it is impossible for me to make the wires (or strings) overlap at only one point.
> Again, the number of points of contact is distinct from the number of spatial turns at a given time slice of a given frame. You are totally confused about multiple elementary things. You just need to think more clearly and pay attention to the patient explanation that has been provided to you.
>
> > So in any scenario where the two plates have no rotation relative to each other...
>
> Wait, you yourself said you begin the plate rotations simultaneously in terms of F1, so they do not begin simultaneously in terms of F0, and so you cannot say they have "no rotation relative to each other" during the period of time of F0 when one is rotating and the other is not. This is how the one turn in the wires is introduced. Understand? (It's so strange than you are having trouble understanding this now, because you seemed to understand it in your previous scenario when the wire was attached to the rotating cylinder, and 10 turns were introduced in terms of F0. Remember?)

Al,
Let's do things one step at a time. If the two wires are attached to the plates as shown in Figure 1 and the plates NEVER rotate and the wires are NEVER detached from the plates, and the wires NEVER loop over either plate, is it possible for the wires to overlap as shown in Figure 2?
David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 2:44:26 PM UTC-7, sep...@yahoo.com wrote:
> If the two wires are attached to the plates as shown in Figure 1 and the plates NEVER
> rotate and the wires are NEVER detached from the plates, and the wires NEVER loop
> over either plate, is it possible for the wires to overlap as shown in Figure 2?

You haven't defined what you mean by the word "overlap" (contact? number of local turns? net turns? other?), but what your brain seems to be struggling to ask is "While the plates maintain a constant relative orientation, N turns apart (in terms of a given frame), is it possible merely by stretching the wires to change the number of net turns in the wires between the plates?" The answer is self-evidently no. This has been explained to you many times before, remember?

At this rate it will take you approximately forever to understand. The entire scenario has been fully explained to you, in detail. What part of the explanation don't you understand? Please pick up the pace.

On Tuesday, June 15, 2021 at 5:36:38 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 2:44:26 PM UTC-7, sep...@yahoo.com wrote:
> > If the two wires are attached to the plates as shown in Figure 1 and the plates NEVER
> > rotate and the wires are NEVER detached from the plates, and the wires NEVER loop
> > over either plate, is it possible for the wires to overlap as shown in Figure 2?
> You haven't defined what you mean by the word "overlap" (contact? number of local turns? net turns? other?), but what your brain seems to be struggling to ask is "While the plates maintain a constant relative orientation, N turns apart (in terms of a given frame), is it possible merely by stretching the wires to change the number of net turns in the wires between the plates?" The answer is self-evidently no. This has been explained to you many times before, remember?
>
> At this rate it will take you approximately forever to understand. The entire scenario has been fully explained to you, in detail. What part of the explanation don't you understand? Please pick up the pace.

If one plate makes one revolution and the other plate makes zero revolutions we get the image shown in Figure 2. The half way point between plate A and plate B shown in Figure 2 shows what I mean by overlap of the two wires. If a frame F1 is moving with velocity V relative to the Figure 2 frame, do frame F1 observers only observe one section between plate A and plate B where the wires overlap like they do in the center of figure 2 or do they observe more than one section where that occurs? We can make V very large. The obvious answer to me is that they only observe that single section as shown at the midway point between A and B has an overlapping of the wires.

David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 4:47:35 PM UTC-7, sep...@yahoo.com wrote:
> If one plate makes one revolution and the other plate makes zero revolutions we get the
> image shown in Figure 2.

Not necessarily. It depends on how you move the parts of the wires. For example, if you force the parts of the wire to remain straight and parallel to the axis in terms of F1, then you will get two helical wires in terms of F0. On the other hand, if you force the parts of the wires to ramp straight to the axis in terms of F0 and twist once around each other and ramp linearly back up to the other plate, then that's how the wires will be configured. What you can say in any case is that the wires will have one net turn between the plates.

> The half way point between plate A and plate B shown in Figure 2 shows what I mean
> by overlap of the two wires.

So, as I suspected, where the wires are in contact with each other, possibly twisting around each other while in direct contact, is what you call "overlap". The English word "overlap" is not descriptive of that condition, but I will make allowances.

> If a frame F1 is moving with velocity V relative to the Figure 2 frame, do frame F1
> observers only observe one section between plate A and plate B where the wires
> overlap like they do in the center of figure 2 or do they observe more than one section
> where that occurs?

What part of the explanation that you've been given a dozen times don't you understand? Again, if you force the parts of the wire to ramp linearly down to the axis and twist once around each other and then ramp linearly back up to the other plate in terms of F0, then in terms of F1 this consists of a descending helical shape with -1/2 turn down to the axis, where it twists +1 turn around the other wire, and then an ascending helical shape with -1/2 turn, for a total of 0 turns in terms of F1.

> The obvious answer to me is that they only observe that single section...

No, that's insane. The description of the wires in terms of F0 and F1 are as explained to you a dozen times, including just above. Is there something about the explanation that is unclear to you?

On Tuesday, June 15, 2021 at 7:40:08 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 4:47:35 PM UTC-7, sep...@yahoo.com wrote:
> > If one plate makes one revolution and the other plate makes zero revolutions we get the
> > image shown in Figure 2.
> Not necessarily. It depends on how you move the parts of the wires. For example, if you force the parts of the wire to remain straight and parallel to the axis in terms of F1, then you will get two helical wires in terms of F0. On the other hand, if you force the parts of the wires to ramp straight to the axis in terms of F0 and twist once around each other and ramp linearly back up to the other plate, then that's how the wires will be configured. What you can say in any case is that the wires will have one net turn between the plates.
> > The half way point between plate A and plate B shown in Figure 2 shows what I mean
> > by overlap of the two wires.
> So, as I suspected, where the wires are in contact with each other, possibly twisting around each other while in direct contact, is what you call "overlap". The English word "overlap" is not descriptive of that condition, but I will make allowances.
> > If a frame F1 is moving with velocity V relative to the Figure 2 frame, do frame F1
> > observers only observe one section between plate A and plate B where the wires
> > overlap like they do in the center of figure 2 or do they observe more than one section
> > where that occurs?
> What part of the explanation that you've been given a dozen times don't you understand? Again, if you force the parts of the wire to ramp linearly down to the axis and twist once around each other and then ramp linearly back up to the other plate in terms of F0, then in terms of F1 this consists of a descending helical shape with -1/2 turn down to the axis, where it twists +1 turn around the other wire, and then an ascending helical shape with -1/2 turn, for a total of 0 turns in terms of F1.
>
> > The obvious answer to me is that they only observe that single section....
>
> No, that's insane. The description of the wires in terms of F0 and F1 are as explained to you a dozen times, including just above. Is there something about the explanation that is unclear to you?

All I am saying is that one of the plates rotates one revolution. When you say force the wires, what are you adding to the scenario?
Thanks,
David Seppala
Bastrop TX

On Tuesday, June 15, 2021 at 7:53:33 PM UTC-7, sep...@yahoo.com wrote:
> > Again, if you force the parts of the wire to ramp linearly down to the axis and twist once around each other and then ramp linearly back up to the other plate in terms of F0, then in terms of F1 this consists of a descending helical shape with -1/2 turn down to the axis, where it twists +1 turn around the other wire, and then an ascending helical shape with -1/2 turn, for a total of 0 turns in terms of F1.
>
> All I am saying is that one of the plates rotates one revolution.

You stipulated, in terms of F0, that one plate begins to rotate after the other plate has completed one revolution. That isn't "all you are saying", it's just one part of your question.

> When you say force the wires, what are you adding to the scenario?

No, your scenario entails the application of forces to the parts of the wire to place them in the configuration that ramps linearly from the plates to the axis at the center. The wires would not just magically configure themselves that way. Remember that any influence can only propagate through the wire at the speed of sound in the wire, and the response of the wire (e.g.., breaking) will depend on the precise acceleration profile and materials properties, but it would not spontaneously be configured as you imagine. To be nicely configured as you are picturing you will need to apply suitable forces to each individual particle of the wire. I'm assuming you understand all this, because I've explained it to you several times (and it's also obvious).

So, with that reminder, do you have any remaining questions?

On Tuesday, June 15, 2021 at 7:53:33 PM UTC-7, sep...@yahoo.com wrote:
> > Again, if you force the parts of the wire to ramp linearly down to the axis and twist once around each other and then ramp linearly back up to the other plate in terms of F0, then in terms of F1 this consists of a descending helical shape with -1/2 turn down to the axis, where it twists +1 turn around the other wire, and then an ascending helical shape with -1/2 turn, for a total of 0 turns in terms of F1.
>
> I am saying one of the plates rotates one revolution.

Right, but that does not suffice to specify the configuration of the wires. This is similar to pushing or pulling on the ends of a solid object and thinking that it will result in Born rigid motion. It won't. You need to apply forces to each part of the object to make it undergo Born rigid motion.. Otherwise there will be intrinsic deformation of the object. Similarly with the wires in this scenario, it is not sufficient to just position the ends of the wires by positioning the plates, you need to specify how all the parts of the wire are to be moved. If you don't specify this, you then need to figure out, from the material properties, bulk modulus, brittleness, mass, diameter, etc., of the wires how they will respond. You are not considering the situation in this much detail, so you simply need to specify that you are applying whatever forces are required to configure the wires the way you want them.

When you say force the wires, what are you adding to the scenario?

It is completing the specification of the scenario, which entails the application of forces to the parts of the wire to place them in the configuration that ramps linearly from the plates to the axis at the center. The wires would not just magically configure themselves that way. Remember that any influence can only propagate through the wire at the speed of sound in the wire, and the response of the wire (e.g., breaking) will depend on the precise acceleration profile and materials properties, but it would not spontaneously be configured as you imagine. To be nicely configured as you are picturing you will need to apply suitable forces to each individual particle of the wire. I'm assuming you understand all this, because I've explained it to you several times (and it's also obvious).

So, in summary, there is no inconsistency whatsoever, and nothing paradoxical or puzzling about this scenario. Do you understand now?

On Wednesday, June 16, 2021 at 10:19:11 PM UTC-5, Al Coe wrote:
> On Tuesday, June 15, 2021 at 7:53:33 PM UTC-7, sep...@yahoo.com wrote:
> > > Again, if you force the parts of the wire to ramp linearly down to the axis and twist once around each other and then ramp linearly back up to the other plate in terms of F0, then in terms of F1 this consists of a descending helical shape with -1/2 turn down to the axis, where it twists +1 turn around the other wire, and then an ascending helical shape with -1/2 turn, for a total of 0 turns in terms of F1.
> >
> > I am saying one of the plates rotates one revolution.
>
> Right, but that does not suffice to specify the configuration of the wires. This is similar to pushing or pulling on the ends of a solid object and thinking that it will result in Born rigid motion. It won't. You need to apply forces to each part of the object to make it undergo Born rigid motion. Otherwise there will be intrinsic deformation of the object. Similarly with the wires in this scenario, it is not sufficient to just position the ends of the wires by positioning the plates, you need to specify how all the parts of the wire are to be moved. If you don't specify this, you then need to figure out, from the material properties, bulk modulus, brittleness, mass, diameter, etc., of the wires how they will respond. You are not considering the situation in this much detail, so you simply need to specify that you are applying whatever forces are required to configure the wires the way you want them.
> When you say force the wires, what are you adding to the scenario?
> It is completing the specification of the scenario, which entails the application of forces to the parts of the wire to place them in the configuration that ramps linearly from the plates to the axis at the center. The wires would not just magically configure themselves that way. Remember that any influence can only propagate through the wire at the speed of sound in the wire, and the response of the wire (e.g., breaking) will depend on the precise acceleration profile and materials properties, but it would not spontaneously be configured as you imagine. To be nicely configured as you are picturing you will need to apply suitable forces to each individual particle of the wire. I'm assuming you understand all this, because I've explained it to you several times (and it's also obvious).
>
> So, in summary, there is no inconsistency whatsoever, and nothing paradoxical or puzzling about this scenario. Do you understand now?

If I have a cylinder, and put two rubber bands from end A to end B, both rubber bands being parallel as shown in Figure 1 of this thread, it is impossible for me to make them end up as shown in Figure 2. So let's say I have a long cylinder made of ice, and two plates at each end made of steel. If I stretch two rubber bands from A to B as shown in Figure 1 of this thread and attach them to the steel plates as in Figure 1, and then the ice slowly melts, how do they end up as shown in Figure 2. Tell me how the rubber bands can overlap if they start out parallel. Explain the steps so that I can do it with rubber bands starting out parallel around a cylinder.

David Seppala
Bastrop TX

On Thursday, June 17, 2021 at 7:12:45 AM UTC-7, sep...@yahoo.com wrote:
> If I have a cylinder, and put two rubber bands from end A to end B, both rubber
> bands being parallel as shown in Figure 1 of this thread, it is impossible for me
> to make them end up as shown in Figure 2.

Nope. It is perfectly possible (even trivial) to, in terms of F0, begin rotating one plate after the other plate has completed one revolution, introducing one net turn, and to force the parts of the wire to ramp down linearly to the center where they twist once around each other. In terms of F1 this is a helical ramp with -1/2 turn as radius is shrinking, +1 turn twisting on the axis, and -1/2 turn helical ramp back up to the disk, for a net 0 turns. We covered this before, remember?

> Let's say I have a long cylinder made of ice, and two plates at each end made of steel.
> If I stretch two rubber bands from A to B as shown in Figure 1 of this thread and attach
> them to the steel plates as in Figure 1, and then the ice slowly melts, how do they end up
> as shown in Figure 2.

You apply to each part of the steel wires -- which behave like rubber bands on this scale -- the forces needed to place them into the configuration noted, just as already explained half a dozen times. Remember?

> Tell me how the rubber bands can overlap if they start out parallel.

In terms of F0, they start out parallel, and then one plate completes a turn before the other starts to rotate, so there is one net turn, and you are applying forces to the parts of the wire to place them in the noted configuration. If you applied other forces, such as attaching them to a cylinder simultaneously in terms of F1, they would remain straight and parallel in terms of F1, and they would become a helix of constant radius in terms of F0.. So the wires can acquire various shapes when you begin rotating the plates, depending on what forces you apply to the parts of the wires. Understand?

> Explain the steps so that I can do it with rubber bands starting out parallel around a cylinder.

As already explained, in detail, multiple times, if you apply forces to the parts of the wire (say, by attaching them to a cylinder simultaneously in terms of F1) so that they wires continue to be straight and parallel in terms of F1, then the wires will become helical with constant radius in terms of F0, and they will not approach the axis or touch each other. On the other hand, if you apply forces to make the parts, in terms of F0, ramp linearly down to the axis and twist once around and ramp linearly back up to the plate, then in terms of F1 the wires will be decreasing helical with -1/2 turn down to the axis, +1 twist, and expanding helix with -1/2 turn back to the plate. Likewise you can apply forces to place the wires in any of infinitely many other configurations, and just as easily describe each configuration in terms of F0 and F1.

Now do you understand? If not, what part of the explanation don't you understand?

On Thursday, June 17, 2021 at 10:48:11 AM UTC-5, Al Coe wrote:
> On Thursday, June 17, 2021 at 7:12:45 AM UTC-7, sep...@yahoo.com wrote:
> > If I have a cylinder, and put two rubber bands from end A to end B, both rubber
> > bands being parallel as shown in Figure 1 of this thread, it is impossible for me
> > to make them end up as shown in Figure 2.
> Nope. It is perfectly possible (even trivial) to, in terms of F0, begin rotating one plate after the other plate has completed one revolution, introducing one net turn, and to force the parts of the wire to ramp down linearly to the center where they twist once around each other. In terms of F1 this is a helical ramp with -1/2 turn as radius is shrinking, +1 turn twisting on the axis, and -1/2 turn helical ramp back up to the disk, for a net 0 turns. We covered this before, remember?
>
> > Let's say I have a long cylinder made of ice, and two plates at each end made of steel.
> > If I stretch two rubber bands from A to B as shown in Figure 1 of this thread and attach
> > them to the steel plates as in Figure 1, and then the ice slowly melts, how do they end up
> > as shown in Figure 2.
> You apply to each part of the steel wires -- which behave like rubber bands on this scale -- the forces needed to place them into the configuration noted, just as already explained half a dozen times. Remember?
> > Tell me how the rubber bands can overlap if they start out parallel.
> In terms of F0, they start out parallel, and then one plate completes a turn before the other starts to rotate, so there is one net turn, and you are applying forces to the parts of the wire to place them in the noted configuration. If you applied other forces, such as attaching them to a cylinder simultaneously in terms of F1, they would remain straight and parallel in terms of F1, and they would become a helix of constant radius in terms of F0. So the wires can acquire various shapes when you begin rotating the plates, depending on what forces you apply to the parts of the wires. Understand?
> > Explain the steps so that I can do it with rubber bands starting out parallel around a cylinder.
> As already explained, in detail, multiple times, if you apply forces to the parts of the wire (say, by attaching them to a cylinder simultaneously in terms of F1) so that they wires continue to be straight and parallel in terms of F1, then the wires will become helical with constant radius in terms of F0, and they will not approach the axis or touch each other. On the other hand, if you apply forces to make the parts, in terms of F0, ramp linearly down to the axis and twist once around and ramp linearly back up to the plate, then in terms of F1 the wires will be decreasing helical with -1/2 turn down to the axis, +1 twist, and expanding helix with -1/2 turn back to the plate. Likewise you can apply forces to place the wires in any of infinitely many other configurations, and just as easily describe each configuration in terms of F0 and F1.
>
> Now do you understand? If not, what part of the explanation don't you understand?
I fully understand how it works from frame F0's point of view.
Please describe how the wires (or rubber bands) overlap from F1's point of view where plate A and plate B start rotating simultaneously and at the identical rotation rate when at time t0' in frame F1 the two wires or rubber bands are shown in Figure 1 of this thread . Do not use any of the F0 observers views, only the F1 frame's observers point of view. I don't understand how the F1 observers say the wire's started out parallel, and eventually they overlapped each other at the midpoint between the two plates.
Thanks,
David Seppala
Bastrop TX

On Thursday, June 17, 2021 at 9:05:55 AM UTC-7, sep...@yahoo.com wrote:
> > As already explained, in detail, multiple times, if you apply forces to the parts of the wire (say, by attaching them to a cylinder simultaneously in terms of F1) so that they wires continue to be straight and parallel in terms of F1, then the wires will become helical with constant radius in terms of F0, and they will not approach the axis or touch each other. On the other hand, if you apply forces to make the parts, in terms of F0, ramp linearly down to the axis and twist once around and ramp linearly back up to the plate, then in terms of F1 the wires will be decreasing helical with -1/2 turn down to the axis, +1 twist, and expanding helix with -1/2 turn back to the plate. Likewise you can apply forces to place the wires in any of infinitely many other configurations, and just as easily describe each configuration in terms of F0 and F1.
> >
> I fully understand how it works from frame F0's point of view.

Great, then you also understand in terms of F1, because the translation from one system of coordinates to another is simple math, not involving any physics at all. I've explained, for each configuration in F0, the corresponding configuration in F1, and vice versa, so you now understand all possible configurations in terms of both coordinate systems.

> Please describe how the wires (or rubber bands) overlap from F1's point of view...

You are applying forces to the parts of the wires to cause them, in terms of F1, to be a helical ramp with -1/2 turn down to the axis, with +1 twist, and then a helical ramp with -1/2 twist back to the plate. We covered this before, remember? (Those are the same forces that, in terms of the coordinates you stupidly tell me not to mention, causes the wires to linearly ramp down, twist one turn, and linearly ramp up, as explained previously.)

> I don't understand how the F1 observers say the wire's started out parallel, and eventually
> they overlapped each other at the midpoint between the two plates.

You don't? You are applying forces to the wires to make them do that. Duh.. Bear in mind that forces transmitted though the wire itself can only propagate at the speed of sound in the wire, which is not nearly fast enough to keep the parts of the wire in mechanical equilibrium on the scale and time-frame involved, so the parts of the wire are essentially independent particles, and you need to apply forces to each particle to configure them as you want them. This is similar to trying to make a solid object undergo Born rigid motion. You can't just push on the end, you need to coordinate forces on each particle. Otherwise you will get deformations that depend on the rate of acceleration and the materials properties, etc.

Your problem seems to be that you think you can perform this with a little string in your stationary hands, which always remains in mechanical equilibrium, and you are not grasping that on the scale and time-frame of the scenario the wires are not nearly in mechanical equilibrium, so you need to force them to whatever shape you want. Attaching to a cylinder simultaneously in terms of F1 is one fully-defined way, but when you remove the cylinder you need to specify what forces are applied to configure the wires. Again, the translation of the forces and configuration from F0 to F1 is pure math, not physics.

Now do you finally understand?

On Thursday, June 17, 2021 at 9:05:55 AM UTC-7, sep...@yahoo.com wrote:
> I fully understand how it works from frame F0's point of view.

Great, then you also understand "how it works" in terms of F1, because the translation from one system of coordinates to another is simple math, not involving any physics at all. I've explained, for each configuration in F0, the corresponding configuration in F1, and vice versa, so you now understand "how it works" for all possible configurations in terms of both coordinate systems.

> Please describe how the wires (or rubber bands) overlap from F1's point of view...

We covered that before (several times). Again, you've stipulated forces applied to the parts of the wires to cause them, in terms of F1, to be a helical ramp with -1/2 turn down to the axis, with +1 twist (which you weirdly call "overlap"), and then a helical ramp with -1/2 turn up to the plate. Do you understand this?

> I don't understand how the F1 observers say the wire's started out parallel, and eventually
> they overlapped each other at the midpoint between the two plates.

You don't? You're not very articulate, so I can only guess why you still don't understand, after it's been clearly explained several times. First, to be sure you aren't being confused by your silly vernacular, this isn't about what some particular "observers say", this is about objective verifiable facts of which everyone is (or can be) aware: In terms of F1, the wires end up configured as a helical ramp with -1/2 turn from plate down to the axis, with +1 twist at the middle, and then a helical ramp with -1/2 turn up to the plate.

If you are having trouble understanding how the shape of the wires continuously evolves from the original two parallel straight wires to the eventual shape, recall that you are stipulating forces applied to the wires to make them do that. Bear in mind that forces transmitted though the wire itself can only propagate at the speed of sound in the wire, which is not nearly fast enough to keep the parts of the wire in mechanical equilibrium on the scale and time-frame involved, so the parts of the wire are essentially independent particles, and you need to apply forces to each particle to configure them as you want them. This is somewhat similar to trying to make a solid object undergo Born rigid motion. You can't just push on the end, you need to coordinate forces on each particle. Otherwise you will get deformations that depend on the rate of acceleration and the materials properties, etc..

Your problem seems to be that you think you can perform this with a little string in your stationary hands, which always remains in mechanical equilibrium, and you are not grasping that on the scale and time-frame of the scenario the wires are not nearly in mechanical equilibrium, so you need to force them to whatever shape you want. Again, the translation of the forces and configuration from F0 to F1 is pure math, not physics.

Hopefully this clears things up for you. If you still don't understand, just ask, and point out what part of the explanation is unclear to you.

On Friday, June 18, 2021 at 2:28:21 AM UTC-5, Al Coe wrote:
> On Thursday, June 17, 2021 at 9:05:55 AM UTC-7, sep...@yahoo.com wrote:
> > I fully understand how it works from frame F0's point of view.
> Great, then you also understand "how it works" in terms of F1, because the translation from one system of coordinates to another is simple math, not involving any physics at all. I've explained, for each configuration in F0, the corresponding configuration in F1, and vice versa, so you now understand "how it works" for all possible configurations in terms of both coordinate systems.
>
> > Please describe how the wires (or rubber bands) overlap from F1's point of view...
>
> We covered that before (several times). Again, you've stipulated forces applied to the parts of the wires to cause them, in terms of F1, to be a helical ramp with -1/2 turn down to the axis, with +1 twist (which you weirdly call "overlap"), and then a helical ramp with -1/2 turn up to the plate. Do you understand this?
> > I don't understand how the F1 observers say the wire's started out parallel, and eventually
> > they overlapped each other at the midpoint between the two plates.
> You don't? You're not very articulate, so I can only guess why you still don't understand, after it's been clearly explained several times. First, to be sure you aren't being confused by your silly vernacular, this isn't about what some particular "observers say", this is about objective verifiable facts of which everyone is (or can be) aware: In terms of F1, the wires end up configured as a helical ramp with -1/2 turn from plate down to the axis, with +1 twist at the middle, and then a helical ramp with -1/2 turn up to the plate.
>
> If you are having trouble understanding how the shape of the wires continuously evolves from the original two parallel straight wires to the eventual shape, recall that you are stipulating forces applied to the wires to make them do that. Bear in mind that forces transmitted though the wire itself can only propagate at the speed of sound in the wire, which is not nearly fast enough to keep the parts of the wire in mechanical equilibrium on the scale and time-frame involved, so the parts of the wire are essentially independent particles, and you need to apply forces to each particle to configure them as you want them. This is somewhat similar to trying to make a solid object undergo Born rigid motion. You can't just push on the end, you need to coordinate forces on each particle. Otherwise you will get deformations that depend on the rate of acceleration and the materials properties, etc.
>
> Your problem seems to be that you think you can perform this with a little string in your stationary hands, which always remains in mechanical equilibrium, and you are not grasping that on the scale and time-frame of the scenario the wires are not nearly in mechanical equilibrium, so you need to force them to whatever shape you want. Again, the translation of the forces and configuration from F0 to F1 is pure math, not physics.
>
> Hopefully this clears things up for you. If you still don't understand, just ask, and point out what part of the explanation is unclear to you.

Using the scenario below, can you clarify your statement " In terms of F1 this is a helical ramp with -1/2 turn as radius is shrinking, +1 turn twisting on the axis, and -1/2 turn helical ramp back up to the disk, for a net 0 turns."
Scenario,
Two plates A and B are spinning at a constant rate of 10 revolutions per second perpendicular to the x-axis as measured in frame F0. Each plate is centered on the x-axis. The plates are separated by a distance L along the x axis of F0. The plates do not vary from their x coordinates as measured in F0. On the x-axis there is a steel rod at rest that extends from Plate A to Plate B. Parallel to the x-axis just above each plate there is a wire that extends from Plate A x coordinate to the Plate B x coordinate. There is an inertial frame F1 moving along the x-axis with velocity V relative to frame F0. V and L are such that simultaneous events as measured in F1 that occur at Plate A and Plate B occur one second apart as measured in frame F0.
Now at time t0' frame F1 observers simultaneously attach each end of the wire to the top of the rotating plates. One end is attached to plate A and the other end is simultaneously attached to plate B. Observers in frame F0 measure that when the wire was attached to plate A, plate A then made 10 revolutions before the other end of the wire as attached to plate B. Now we begin shortening the wire by pulling it through a hole in Plate A where it was initially attached to. Plate A and Plate B are massive so the separation between the two plates remains a distance L apart.
As the wire is shortened, it wraps around the steel rod that is sitting at rest on the x-axis. This process is continued until the wire contacts the rod at 10 points along the x-axis as observed in frame F0.
Please use your explanation of events as viewed in F1 to explain why F1 observers initially observed the wire to be parallel to the x-axis, then attached to each plate simultaneously at time t0' and are initially parallel at time t0' to the x-axis, but after the wire was shortened now make contact at 10 points of the rod that is at rest along the x-axis between plate A and plate B.
Thanks,
David Seppala
Bastrop TX

On Friday, June 18, 2021 at 11:08:56 AM UTC-7, sep...@yahoo.com wrote:
> Using the scenario below, can you clarify your statement " In terms of F1 this is a helical ramp with -1/2 turn as radius is shrinking, +1 turn twisting on the axis, and -1/2 turn helical ramp back up to the disk, for a net 0 turns."

Ah, I see your confusion. Each explanation of the shape of the wires for a given scenario applies to the shape of the wires for that scenario. In different scenarios the wires have different shapes. In the scenario under discussion in this thread (your simplified knotty question), one plate begins rotating in terms of F0 after the other plate has completed 1 rotation, and you are applying forces to the parts of the wire to make them, in terms of F0, ramp linearly from plate to axis, twist once around the other, and ramp linearly back up to the other plate. You asked how this configuration is described in terms of F1, and the answer is as given in the quote above. Since you have abandoned that scenario now, I assume you finally understand it. You're welcome.

> As the wire is shortened, it wraps around the steel rod that is sitting at rest on the x-axis. This
> process is continued until the wire contacts the rod at 10 points along the x-axis as observed
> in frame F0.

As suggested the last time you raised this old "10 points of contact" claim, it would be helpful for you to try to draw a picture of how you are imagining that the wire is shaped. In order for there to be 10 distinct points of contact, you will need to apply a very weird distribution of forces to the parts of the wire, to cause the wire to bend alternately toward and away from the central axis. It's certainly theoretically possible to force the wire into such an oscillating helical shape, but it would not arise simply by pulling on the end of the wire. (It would be more natural for the wire to wind like a barber pole around the central rod, but you're free to force the wire into any shape you like.) Regardless of the forces required to configure the wire in any particular way, the translation of the description from F0 to F1 is trivial math.

So, go ahead and describe (with a picture if necessary) what shape you are going to have in terms of F0, and then I will perform the simple grade school algebra and tell you the description of that shape in terms of F1.

On Friday, June 18, 2021 at 2:21:15 PM UTC-5, Al Coe wrote:
> On Friday, June 18, 2021 at 11:08:56 AM UTC-7, sep...@yahoo.com wrote:
> > Using the scenario below, can you clarify your statement " In terms of F1 this is a helical ramp with -1/2 turn as radius is shrinking, +1 turn twisting on the axis, and -1/2 turn helical ramp back up to the disk, for a net 0 turns."
> Ah, I see your confusion. Each explanation of the shape of the wires for a given scenario applies to the shape of the wires for that scenario. In different scenarios the wires have different shapes. In the scenario under discussion in this thread (your simplified knotty question), one plate begins rotating in terms of F0 after the other plate has completed 1 rotation, and you are applying forces to the parts of the wire to make them, in terms of F0, ramp linearly from plate to axis, twist once around the other, and ramp linearly back up to the other plate. You asked how this configuration is described in terms of F1, and the answer is as given in the quote above. Since you have abandoned that scenario now, I assume you finally understand it. You're welcome.
> > As the wire is shortened, it wraps around the steel rod that is sitting at rest on the x-axis. This
> > process is continued until the wire contacts the rod at 10 points along the x-axis as observed
> > in frame F0.
> As suggested the last time you raised this old "10 points of contact" claim, it would be helpful for you to try to draw a picture of how you are imagining that the wire is shaped. In order for there to be 10 distinct points of contact, you will need to apply a very weird distribution of forces to the parts of the wire, to cause the wire to bend alternately toward and away from the central axis. It's certainly theoretically possible to force the wire into such an oscillating helical shape, but it would not arise simply by pulling on the end of the wire. (It would be more natural for the wire to wind like a barber pole around the central rod, but you're free to force the wire into any shape you like.) Regardless of the forces required to configure the wire in any particular way, the translation of the description from F0 to F1 is trivial math.
>
> So, go ahead and describe (with a picture if necessary) what shape you are going to have in terms of F0, and then I will perform the simple grade school algebra and tell you the description of that shape in terms of F1.
Okay,
Let's say it winds around the central rod like a barber pole so that at time t1 as measured in the F0, 10 points have the same y,z coordinates.
David Seppala
Bastrop TX

On Friday, June 18, 2021 at 4:15:42 PM UTC-5, Al Coe wrote:
> On Friday, June 18, 2021 at 1:15:58 PM UTC-7, sep...@yahoo.com wrote:
> > Let's say it winds around the central rod like a barber pole so that at time t1 as measured in the F0, 10 points have the same y,z coordinates.
> So now the "10 points of contact" have been discarded again? Remember, in April 2019 you raised the "10 points of contact" idiocy, and I pointed out that you couldn't possibly mean that, and you were embarrassed and admitted that, as I suggested, you really meant it winds around 10 times like a barber pole, and I graciously accepted that you had just experienced a brain fade when you described that as "10 points of contact". I then explained how the barber pole is described in terms of F1, and then you ran away. Now here you are, over two years later, and you raise the "10 points of contact" again, only to retract it again, and admit that you really mean winding like a barber pole. And you ask me to explain (yet again) how this is described in terms of F1. And you run away from the explanation of your simplified knotty question? What on earth is wrong with you?
>
> For the umpteenth time, for a wire that, in terms of F0, ramps from the plate connection linearly to the central rod, spirals around the rod like a barber pole 10 times over some axial span, and then ramps linearly back up to the plate, this is described in terms of F1 as a descending helical shape through -q turns down to the rod, then +2q turns on the rod, and then an ascending helical shape with -q turns back up to the plate. The value of q depends on the point of the rod where the linear ramp reaches the rod. I gave you the values for the two extreme cases of (1) ramping to the center, and (2) ramping to the ends. Remember?
>
> This has been explained to you repeatedly over the past two years. If this is still unclear to you, please say what part of the explanation you still don't understand.

In your explanation, you state that in terms of F1 there is -q turns, then + 2q turns, then -q turns. But you never explain in terms of F1, how they observe the parallel going around the rod -q turns and then switching to +2q turns. You simply say that's the Einstein's theory works. Tell me how for example, -5 turns occurs as viewed in F1 over a given distance and then it switches to +2q turns. Explain the motion of points of the wire as observed in F1 and what forces cause this to occur and why for example its not -2q turns and then +2q turns to wind up zero.

David Seppala
Bastrop TX

On Friday, June 18, 2021 at 6:10:22 PM UTC-5, Al Coe wrote:
> On Friday, June 18, 2021 at 3:09:25 PM UTC-7, sep...@yahoo.com wrote:
> > > For a wire that, in terms of F0, ramps from the plate connection linearly to the central rod, spirals around the rod like a barber pole 10 times over some axial span, and then ramps linearly back up to the plate, this is described in terms of F1 as a descending helical shape through -q turns down to the rod, then +2q turns on the rod, and then an ascending helical shape with -q turns back up to the plate. The value of q depends on the point of the rod where the linear ramp reaches the rod. I gave you the values for the two extreme cases of (1) ramping to the center, and (2) ramping to the ends. Remember?
> > >
> > In your explanation, you state that in terms of F1 there is -q turns, then + 2q turns, then -q turns.
> Right! And you understand, right?
>
> > You never explain in terms of F1, how they observe the parallel going around the
> > rod -q turns and then switching to +2q turns.
> That is not true, I've explained it many times. Again, you are applying forces to the parts of the wire to displace them from the original parallel shape to the final shape. You don't really mean "how they observe", e.g., with opera glasses, what you mean (presumably) is how does the wire deform from one shape to the other? Well, that's what I just explained. You begin with a striaght wire parallel to the axis in terms of F1, and you push and pull on the parts of the wire until you have arranged those parts so that they are arranged as a descending helical shape through -q turns down to the rod, then +2q turns on the rod, and then an ascending helical shape with -q turns back up to the plate.
>
> What other answer could there possibly be? It has the shape it has because you bend it into that shape. Duh. Can you explain why your brain is incapable of grasping this simple statement of fact?
> > You simply say that's the Einstein's theory works.
> That is a lie. The point you are having trouble understanding really has nothing to do with special relativity. You are having trouble grasping the fact that if you bend a wire into a particular shape then you will have bent the wire into that particular shape. Your inability to grasp (or accept) this tautological fact goes much deeper than just inability to understand physics.
> > Explain the motion of points of the wire as observed in F1 and what forces cause
> > this to occur and why for example its not -2q turns and then +2q turns to wind up zero.
> Oh my goodness. These aren't just random numbers. Remember, in terms of F0 the wire ramps linearly (no turns) down from one plate to the axis at some point, then spirals around the axis (10 turns) for some span, and then ramps linearly (no turns) up to the opposite plate. Now, because of the skew of simultaneity between F0 and F1, there are 10 turns per distance between plates, which is uniform over that distance. So, letting the middle spiraling segment cover the fraction x of the distance between plates, each ramp covers (1-x)/2 of the distance, and hence in terms of F1 on each ramp we have 0 - 10[(1-x)/2] turns and on the center segment we have 10 - 10x turns, for a total of 0 turns.
>
> If anything about this is still unclear to you, just ask.

Let's do a very simple scenario. A piece of rubber or (something stretchable ) extends from A to B just above the plates. Let's make that piece of rubber 1 cm wide (y direction), 1 mm thick (z direction), and of length L (x direction) as measured in F0. Plates A and B are rotating 10 revolutions per second as measured in F0. Again events that occur simultaneously in F1 at A and B occur 1 second apart in F0. At time t0' observers in F1 simultaneously attach the piece of rubber to the top of each rotating plate. Now in F0, after a steady state condition is reached, the piece of rubber as viewed in F0 is basically parallel to the x-axis at any point in time but now the piece of rubber has 10 twists in it along this parallel line.
Describe how F1 observers view the piece of rubber and how F1 observers explain where the 10 twists came from.
Thanks,
David Seppala
Bastrop TX

On Friday, June 18, 2021 at 7:45:25 PM UTC-5, Al Coe wrote:
> On Friday, June 18, 2021 at 4:58:43 PM UTC-7, sep...@yahoo.com wrote:
> > > In terms of F0 the wire ramps linearly (no turns) down from one plate to the axis at some point, then spirals around the axis (10 turns) for some span, and then ramps linearly (no turns) up to the opposite plate. Now, because of the skew of simultaneity between F0 and F1, there are 10 turns per distance between plates, which is uniform over that distance. So, letting the middle spiraling segment cover the fraction x of the distance between plates, each ramp covers (1-x)/2 of the distance, and hence in terms of F1 on each ramp we have 0 - 10[(1-x)/2] turns and on the center segment we have 10 - 10x turns, for a total of 0 turns. If anything about this is still unclear to you, just ask.
> >
> > Let's do a very simple scenario.
> You earnestly asked me to explain the numbers of net turns for various ramp lengths, and when I do (you're welcome), you totally ignore it and jump to yet another simple scenario. I've patiently given you the detailed explanations of your simple scenarios #1 through #47, and now you are going on to simple scenario #48, never having had the intellectual integrity (not to mention personal decency) to acknowledge that all your questions have been answered and your misconceptions debunked.
>
> > A piece of rubber ... [...stupidly described simple scenario #48...]
>
> Look, if in terms of F0 you attach one end of a ribbon to one spindle, and then after 10 turns you attach the other end to the other spindle, the ribbon will have 10 net twists in it in terms of F0, but it will have 0 net twists in terms of F1 (in which you attached the ends of the ribbon simultaneously). Understand?

You replied,"Look, if in terms of F0 you attach one end of a ribbon to one spindle, and then after 10 turns you attach the other end to the other spindle, the ribbon will have 10 net twists in it in terms of F0, but it will have 0 net twists in terms of F1 (in which you attached the ends of the ribbon simultaneously). Understand?"
I understand that's how the transform works, but I don't understand how that is physically possible. If for example, the top side of the piece of rubber is white and the other side is red, if F1 says that the piece of rubber has zero twists then the red side is never at a coordinate that has a radius greater than the white side. However F0 says that there are points where the red side is at a radius greater than the white side. Do you understand? If so explain which frame has the correct view.
David Seppala
Bastrop TX

On Saturday, June 19, 2021 at 1:05:34 AM UTC-5, Al Coe wrote:
> On Friday, June 18, 2021 at 8:25:42 PM UTC-7, sep...@yahoo.com wrote:
> > > > In F0, after a steady state condition is reached, the piece of rubber as viewed
> > > > in F0 is basically parallel to the x-axis at any point in time but now the piece of
> > > > rubber has 10 twists in it along this parallel line. Describe how F1 observers view
> > > > the piece of rubber and how F1 observers explain where the 10 twists came from.
> > >
> > > If in terms of F0 you attach one end of a ribbon to one spindle, and then after 10 turns you attach the other end to the other spindle, the ribbon will have 10 net twists in it in terms of F0, but it will have 0 net twists in terms of F1 (in which you attached the ends of the ribbon simultaneously). Understand?
> >
> > I understand that's how the transform works, but I don't understand how that is
> > physically possible. If for example, the top side of the piece of rubber is white and
> > the other side is red, if F1 says that the piece of rubber has zero twists then the
> > red side is never at a coordinate that has a radius greater than the white side.
> As always, you are trivially mistaken. You didn't ask in the previous post about the radial position of the band, you asked about the twists, and the trivial answer is as given above, independent of the radial positions. Now you are asking yet another question, namely, how the radial position of the band is described in terms of F1. Again, the answer is trivial:
>
> Since you are forcing the centerline of the band to be straight and parallel to the plate's axis of rotation in terms of F0, it is in a helical shape with ten loops in terms of F1, with the band maintaining a fixed orientation relative to the plates. Thus the band is not twisted, but the red side is alternately on the side closer to the plate axis and on the side further from the plate axis, alternating ten times along the length.
>
> In summary: In terms of F0, the band is straight and twisted; in terms of F1 the band is helical and untwisted. These are just two different descriptions of the same thing, in terms of two different coordinate systems. All of this has been covered many times previously. Now do you finally understand?
> > Describe how F1 observers view the piece of rubber and how F1 observers explain
> > where the 10 twists came from.
> Again, the band is not twisted in terms of F1, the centerline of the band has a helical shape around the plate axis. See above. If there is something about this that you still don't understand, just go ahead and ask.

Its unclear to me how you define the helical shape of the centerline in terms of F1. If the piece of rubber has a small hole along the length L along the centerline as viewed in F0, when the steady-state condition is reached, a very small object could be fired along the x-axis and travel from A to B through this hole without hitting the piece of rubber. The speed of this object could be any speed and the result would be the same. Please explain how that would work with a helical shaped centerline in terms of F1.

Thanks,
David Seppala
Bastrop TX