Influx wrote:So I guess, it could actually be said that time measures motion. Circular reasoning?
Time doesn't measure anything, time is just defined as distance-traveled by one object as a reference standard traverses a unit distance.
Influx wrote:Yes I do, but it makes no sense to take it out of context. What I said is in relation to the distance covered by different size clocks that display the same time unit. The hands of Big Ben in London will cover a lot more distance than a wrist watch in the passage of the same amount of time units.
But when we quantify time we use *one* reference standard, a single clock. If we define an hour to be a specific distance-traveled by the hand of Big Ben, that's what it is, by definition.
If, as Big Ben's hand goes from A to 7*A, your wrist watch hand goes from A to 2*A then we say that your wrist watch hand is moving at 1/6 the velocity of Big Ben's hand. In other words, your wrist watch hand takes 6 times as long to traverse the unit distance as Big Ben's hand. Big Ben took 1 unit of time to traverse 6*A, your wrist watch would take 6 units of time to traverse 6*A if it continued moving as it has.
So, time is just defined in terms of unit distances-traveled by an object compared to the distance-traveled by a reference standard.
Influx wrote:Or am I to understand that motion measures motion?
No, motion doesn't measure anything either. Motion is "two or more locations of an object". We measure successive locations of an object, call it distance-traveled, and compare it to the successive locations of another object. This comparison yields relative velocity and its mathematical and conceptual inverse, time.
Influx wrote:That is, I can use the clock to measure how much time there was no motion, as in, say, my coffee cup, it sat on my table without motion for an hour. See, in this case I did not use the motion to measure the non motion of the coffee cup, but rather the time units, i.e. time, the concept of time... Aww jeez I give up.
First off, the cup is moving by definition. Motion is two locations of an object and location is the set of distances from an object to every other object. If the hand's location is changing the cup's is changing too, by definition.
So let's examine this carefully. We have a universe of two objects, one called a cup and one called a hand. The hand traverses some distance. By definition, the cup is moving too because motion is two or more locations of an object and location is the set of distances between an object and every other object. So as the hand moves the cup's location changes, the cup is moving by definition. As the hand moves a unit distance so does the cup, the distance-traveled by one is always equal to the distance-traveled by the other. So the cup traverses A as the hand traverses A. The time for the cup to traverse A is the same as for the hand to traverse A, and their relative velocity is just 1. The hand traverses 60*A, what does this mean? It means the cup traversed 60*A. We do not get very far trying to quantify time with only two objects.
We need at least a third object, maybe called a person, to measure a difference in velocity, and thus quantify time. As the hand moves, it traverses a distance A away from the cup and a distance 2*A away from the person. As the hand (or the cup) traverses A the person traverses 2*A. We define the "time" for the person to traverse A as A/2*A = 1/2 = 0.5. We define the person's velocity as 2*A/A = 2.
The reason you associate the ticks of a clock, by itself, with time is because it is so very familiar to you. If you tell someone who knows nothing of your clocks that the clock ticked 14 times they have no idea what you're talking about. If you pull it out and let it tick 14 times the only way the person understands this is due to the motion of objects around him which s/he is familiar with. Additionally the person's brain has something like an internal timer. The distance-traveled by various signals in the brain are associated with events in the person's past. This does not have be be a conscious activity.
In the end, to quantify time you will have to deal with the motion of at least two objects. To do anything useful you will have to talk about the motion of at least three objects. Defining time will involve comparison of distances-traveled.