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A 'simple' Physics postulation...
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TimFox:
One can express the vector velocity v in terms of its three scalar components vxx + vyy + vzz
where v is the velocity, and x, y, and z are "unit vectors" in the three Euclidean directions.
The components vx, etc., can be positive, negative, or zero, but the magnitude of the vector v cannot be negative.  If not moving, the magnitude of v in that reference frame can be zero.
TerraHertz:

--- Quote from: Ian.M on July 09, 2021, 01:50:57 pm ---At the poles, for an infinitesimal instant at the apex of its vertical trajectory, it has zero velocity.  Its speed with respect to the surface is a continuous function so how else is it going to get from positive (distance increasing = ascending) to negative (distance decreasing = descending) without going through zero speed?

--- End quote ---

You're only considering the Earth's rotation. But that is a meaningless exclusion. There are other imposed motions: The Earth's orbit around the Sun (which is a complex spiral due to motion of the solar system) and influences of other objects such as the Moon and other planets.

Glen's question only applies to a hypothetical system of two masses in an infinite void. Initially set in motion moving apart, but not fast enough for gravitational escape. Yes, they both stop and reverse. But then you get into questions of quantum physics, and what is the smallest units of time, space and velocity you can theoretically measure. Even for atomic particles there are limits, and for macroscopic objects with non-zero thermal motion of the component parts, good luck.
Alex Eisenhut:
When Captain Picard orders a "full stop" of the Enterprise 1701-D, does it stop?

Rick Law:

--- Quote from: GlennSprigg on July 09, 2021, 10:58:32 am ---In reference to JUST the local surface of the Earth where you stand, (NOT the solar system, galaxy etc!!)...
If you were able to throw an object 'exactly' vertical, such that it came back to you due to gravity, did the
object ever 'Stop' at it's apex??  Obviously, it can't have, even for 1/1000000000-th of a second, as that would
defy the laws of physics. So it is only ever going up, or coming down. Without stopping!!?   :phew:

--- End quote ---

Think of this problem as looking at a video of the event.  You can measure where the object is on each frame, but in between frames, you don't know for sure.  That is how nature works.  In the case of a video, you can increase the frame rate and get more resolution.  In the case of Nature, there is a point where you cannot speed up the frame rate anymore.  There is a limit to the resolution one can get out of Nature.

When one uses Newtonian mechanics to describe an object's travel, one cannot take that solution to apply it to the very fast (near speed of light), very small (quantum scale, or the even smaller Planck length), or very quick  (Planck time).

What is stop?  One cannot define position smaller than one Planck length (about 1.6x10-35m), nor can one define time duration smaller than one Planck time (time it takes a photon to travel one Planck length).  So is a particle moving when it is wiggling within a cube where each side of the cube is one Planck length?  There is no answer to that question.  Can something happen quicker than one Planck time?  There is no answer to that question because you cannot measure time less than a Planck time.

That is the resolution Nature is willing to give.

So, at the best nature can offer is: the object went UP to within one Plank-length to the top, for a period of one Planck time, we don't know exactly what happened.  By next Planck time, the object is moving down.  That is the theoretical best one can do, if one can indeed get that accurate.
Brumby:

--- Quote from: TerraHertz on July 09, 2021, 11:30:19 pm ---You're only considering the Earth's rotation. But that is a meaningless exclusion. There are other imposed motions: The Earth's orbit around the Sun (which is a complex spiral due to motion of the solar system) and influences of other objects such as the Moon and other planets.

--- End quote ---
I did think that as well, but considered the polar perspective was far enough.


--- Quote from: Rick Law on July 10, 2021, 12:00:46 am ---One cannot define position smaller than one Planck length (about 1.6x10-35m), nor can one define time duration smaller than one Planck time (time it takes a photon to travel one Planck length).
--- End quote ---
Also crossed my mind, but I constrained my journey down that track with: Define "stop".
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