If a step one lands on beat one,

and we know that a "step" is defined to begin when the moving foot passes the standing foot,

then,

during what beat of the music does the travel of the moving foot from passing the old standing foot until it lands in its new place occur.

obviously, the later portion of beat 3 !!!

That's right folks, step one begins during the later part of beat three. If it began only during beat one then either

a) you aren't landing on the beat or

b) you are confused about what what is defined as the beginning of a "step"

Sure. Step one has to start on beat three. Some people count it "three and" but it is still the last part of beat three. Is all due to the definition where a step starts and ends.

Alex Moore writes:
“Step. This usually refers to one movement of the foot, although from a “time value” point of view this is incorrect. In the case of walk forward or backward, for instance, the time value of the step is not completed until the moving foot is drawn up to the foot supporting the weight, ready to commerce another step.”

Does not a “time value” point of view mean the same as a “beat value” point of view.

If a step lands on a beat? How is a beat defined? Could a beat be one swing of a metronome from left to right. Could landing on a beat mean landing on the instant the swing of the metronome is on half way of its movement. Then if a beat and a step lasts 60 cs the step should land on instant 30 sc and the step could begin on instant 0 cs when feet pass and end on instant 60 cs feet passing ready to commerce another step.

SQQ. I am more into Latin. I think there is a simularity to when does a beat end and all that.
This is the way we are taught which I think is easier to understand. During Rumba Walks the coach has two pieces of ebony looking wood that Latin Bands have. He strikes them in time with the music dead on the beat. We must have the whole of the foot on the floor on the stroke, any other way will put us behind the beat and therefore chasing it. Here is the difference . We arrive on four and hold that position and hold it as long as possible and than at the last instance catch the beat of two. The hips do not stop moving.
So in modern we have people playing with the beat. I know that John Wood and another still at the top arrive behind the beat on one. So there we have it , but don't arrive late on two or three.

"If a step lands on a beat? How is a beat defined? Could a beat be one swing of a metronome from left to right. Could landing on a beat mean landing on the instant the swing of the metronome is on half way of its movement. Then if a beat and a step lasts 60 cs the step should land on instant 30 sc and the step could begin on instant 0 cs when feet pass and end on instant 60 cs feet passing ready to commerce another step."

Quite plausible - but it has the following implication some here apparently don't like.

If the part of the beat where the foot lands (30 sc) is "one" then the part of the beat where the step starts (0 sc) is "and" - specifically it is the "and" of the PREVIOUS beat. In other words, you've just described counting "and one".

Have you guys worked out that on a forward step the heel lands first then the ball. One the heel has landed ,and, the ball lands. Then during that, and, the rear foot is moving. And we have to count and one and. Foxtrot and one two and. I've just put this in to keep you guys rolling. It's as good as watching TV.

Sure, if you want to plant your step 1 on beat one, you have to start moving on 3&. Is there a problem with this.? natural turn waltz, lowering on 3& the left foot (man) is just starting to move back ready to plant on the next beat (4, or 1 of the next bar).
It's comforting to konw that Anon is getting pleasure from these posts!! No TV licence needed either

Sometimes it's hard to understand what you are saying when you don't prove-read / edit your messages. Perhaps you could provide us with a time line chart where the beats are used as the axis. Then along this line sketch in where you say each step starts, where the feet passes, where each foot is planted, etc...

ie:

!_________!__________!__________!
3 1 2 3

Guest. With your chart I can tell you exactly where John Wood's left foot is On one the RF foot is on the mark. On (and) the left foot is alongside and the step is turning. The left foot is roughly seven inches apart but the thighs are together. Second Part. The turn is completed and the left foot is stepping on two. The closing foot draws up on the (and) count. Third Part. The body feet knees are up on three and lower on the (and) count. On the (and) count the LF has been released and is roughly 12 inches to the rear on the toe, the ladies feet are together and lowered. The part that most do not understand is the compression on one (and). The knee is bent and the power is used to take him onto step two. There are no tapes where this is done any differently, they all drive off the (and)count. So we have two drives. The second is called Swing. So we drive onto one and we swing from compression on two. Some may argue that Swing is not Drive. The souce of the power comes from the same technique. One more thing. The (and) counts are used as a collection points. Or balance points if you wish to call them that.

"On one the RF foot is on the mark. On (and) the left foot is alongside"

I wonder if you realize that you have just confirmed that the formal step of the left foot begins on the "and" after one. If the feet indeed pass on this and, then that is where the step begins and you should count it "and two"