What is the highest acceptable delay in your opinion between the moment a fault is committed and the moment the shuttle is hit again during service (expressed in seconds)? What is the accepted interpretation of the rules in competitions?
Stradrider: From a physical standpoint this is impossible if you read the question correctly. Neither you nor the shuttle can move from the position you have when a point is scored to the position you have when the shuttle is hit again with no delay. I believe the rules say "no UNDUE delay".
It would be interesting if we could list all things that are or may be considered as "due delay", with evidence of what is factually happening on tournament videos with famous players. I created a thread for that purpose at the following link of you'd like to contribute or read the answers: https://www.badmintoncentral.com/forums/index.php?threads/list-of-due-delays-before-serving.180545/
"Delay" is when you are wasting time. The time from when the shuttle is not in play until the service cannot be called a "delay" as it is a necessary time for you to start the next rally. There is no maximum permitted time between the rallies as it all depends on the situation and the players. You are supposed to pick the shuttle and go to the service line and serve without delay. It is not allowed to work around, going to the back line or to your bag or to discuss strategy with your coach or friend (other than a few words on the way to the service line without stopping), you also cannot just stay on place. The things that can be allowed to do between the rallies - change of shuttle, wiping the floor of sweat, very quick toweling if you are visibly sweating. Umpire will rarely allow powdering the grip as it delays the game quite a bit. The "undue delay" in the rule 9.1.1 you were mentioning only means that when you are in ready position for service you should serve immediately. The unspoken limit for this is 5 seconds but in reality it also varies depending on the players and the feel of the game...
You are making a valid point in bringing up the discussion about the definition of delay. In physics* for instance, a delay is the lapse of time between two events. It's a very personal thing but I think of badminton mainly in terms of physics as it is a prime example of the interplay of many low level laws of physics. Applying the same definitions as in physics also confers the advantage of allowing for a very factual (and thus fair and constant) interpretation of the rules. *See propagation delay for instance, the length of time between the moment the signal leaves the sender (event 1) and reaches the receiver (event 2). https://en.m.wikipedia.org/wiki/Propagation_delay?wprov=sfti1
There is no need to be qualified for discussing any concept, no matter how complex (and I believe that the physics at hand is at the reach of virtually anyone who cares to understand).
OP posits the question like, if we had a timer of n seconds, it will be the grounds to call delaying. But really this is subjective, and it's the umpire's job. It's to his discretion if he feels that a party is causing 'delay'. Many things factor in, as you would have known, and it will change throughout the game.
At least internally discussion is part of our way to build a mental representation of concepts. If we had to be qualified in order to discuss a concept we would never learn anything.
This is a nonsense question as there is no time limit given in the laws. Also, the fault may be committed by a net play (recall the Axelsen-Tien incident?) after which the referee came on court. Fault may also be interpreted by umpire for arriving late on court after interval (All England 2019, anyone?), after which the referee came on court. Or a fault may be committed by shuttle getting slung in the racquet (has happened), after which the player must change racquet, but wait, the player must also cut the strings of the 'slung' racquet. Fault committed by touching net or sliding under, after which the court must be wiped. Fault could also be committed by shuttle staying on the ceiling (or supports), and new shuttle not available, as umpire overlooked. Fault committed by hitting the net, or post, that it must now be checked for proper height. I will keep other faults (that also require sanctions) out of this list for now. All these post-fault situations take time. This time is not marked or counted by the umpire. It is also not counted by any technical official in the arena. Why? Mainly as it is not required by law. Fault leading to disqualification is another situation where there will not be any service. If you consider that that player will serve again, and to the same opponent(s), it will definitley be at another event.
Please stop changing topic. You start with delay in badminton, then veer off topic to delay in physics. I am all for expressing opinions, and fully understand your metaphor. However, you are also comparing a sport (badminton) to a fundamental discipline (physics). Here's wishing you get this message without delay.