Are they the same?
We count time using motion of, e.g., arms of a clock. Motion is described using time as a parameter. But I think motion as such is not the same thing as time.
I'm inclined to think they are the same. Well not exactly the same. Only that time is the best we can do in the face of motion. Motion being infinitly divisible. Time being the constraining of that motion.
As it is now - Our sense of time is based on cycles of motion. I.e. The Earths rotation, the Earth revolves around the sun, the moon revolves around the Earth. A cesium clock is not any different.
We place points on these motions where there are no points.....there being an infinity of them available.
Time would be a man made operation. A tick tick tick approach to the fluid operation of motion. The constraining of motion in a cycle or segment.
While they are tightly linked together I do not see how they could be considered the same. Motion is a result of time, it is not clear that time is a result of motion. For them to be equivlent that realtionship would have to go both ways.
Motion is the result of time?
uniform motion is obviously directly proportional to time. but motion is a function of time and distance.
Motion involves a change in postion and a change in time. Thus to move implies time has passed.
motion is a function of time and distance?
Only after you establish a constraint of motion, and that constraint is the measure we use (the motion of the Earth, and a further segmentation of that motion I.E. hours minutes seconds) otherwise known as our man made agreed upon by everybody segments of time. Your individual sense of that time is also based on another constrained motion (Your own bodily functions). Your individual sense is compared to the agreed upon constraint.
If motion stopped - There would be no time (no events to base an understanding).
Time is an event.
Motion is a continuous event.
Lets try it a bit more simple and fundamental.
Time is (originally, i.e. from nature) the sequence of events. This is a fundamental understanding for which I do not see any further possible mental reflexion.
We humans want and need to quantize time. We do it by using periodic motions which we assume to be constant. That worked well up to the detection of relativity.
Now we know that periodic motions (starting in the innerst part of elementary particles) are no longer constant if these particles are moved. This changes necessarily the time measurement and this caused Albert Einstein to state that "time is dilated" at motion. Time is not dilated but its measurement is.
I hate to get picky here,but I feel it is germane to the discussion.
Lets reflect at least a little.
Rather - Time is based on two events (a beginning and an end) not a sequence. Essentially pick your poison. One rotation of the Earth. One revolution of the earth around the sun. Spitting on pavement?
The (passage) of time is based on a sequence of your chosen paired events where those two events remain by agreement constant, and are repeated. This is not in tune with reality, for time is simply a guess (futile attempt) at the reality of motion (an infinity of events). There being an infinity of events between any two events you so choose to use as a base for time where no paired events can be equal to another pair of events. our degree of understanding of time is limited most likely to planck length. Our understanding of motion is likely limited to this same length, or the depths of our imagination.
One could imagine an infinite sequence of events to the point of a continuous operation of motion.
I would argue that time is dilated, because time is that measurement, and if you try to take that measurement to another location. You will get a skewed result, for no two paired events (constrained motion) can be the same.
You can put a noose around two events, but when the noose drops past the Planck - The noose tightens beyond measure with no room to breathe. There is still however plenty of room to squirm and kick the feet - You just have to imagine every wriggle of every kick.
I would prefer to say that the measurement of time is changed, not the time itself, for the following reason:
There are good arguments to assume that the inner part of an elementary particle is permanently oscillating with the speed of light c. This follows for the electron from the Dirac function, and the same can be computed from the magnetic moment of the electron. There are no good arguments to say that this is different for a quark.
If this is true then the time dilation found in measurements is a direct consequence of this internal motion without any need to change our original understanding of the time itself. Assume that the inner part in a particle is circling with c in relation to your reference system. Now assume that this particle is moved into an axial direction with some speed v. Then this motion is no longer on a circle but on a helix. As the speed of the moving part must maintain the speed c, the circulation period is necessarily dilated. If you calculate this dilation, the change is exactly as given by special relativity.
In this way we can understand the phenomena of special relativity without giving up our original understanding of time (and of space, of course).
Separate names with a comma.