The spatial measurement is not arbitrary because it must be determined relative to two empirical boundaries, as the distance between them, although the choice of things to measure from may be arbitrary, making the determination arbitrary in a relative sense.

The temporal measurement is completely arbitrary because there are no boundaries within time, so the choice, which designates a spatial positioning as starting and ending point is arbitrary in an absolute sense.

The spatial measurement is not arbitrary..................The temporal measurement is completely arbitrary. — Metaphysician Undercover

It is interesting that since 2019 the metre has been defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

Even distance cannot escape from time.

I think you're missing the point. It's not an issue of whether distance can escape from time. It obviously cannot, as things move therefore distances change, with the passing of time. Nevertheless, things in space have definable position, even if moving, and that provides the basis for spatial measurement. On the other hand, the points in time which serve as the boundaries for measurement are totally arbitrary. So, for example, 1/299 792 458 of a second is completely arbitrary.

Nevertheless, things in space have definable position, even if moving, and that provides the basis for spatial measurement. On the other hand, the points in time which serve as the boundaries for measurement are totally arbitrary. — Metaphysician Undercover

An object, or a particle, in space and time can only be at one position at one time (ignoring any debate in quantum mechanics). In other words, a particle in space and time at one moment in time can only be in one position.

I am using the word "arbitrary" as used in your post.

At one moment in time, if a particle is at position A in space then it cannot be at position B in space.

As position A is not position B, there is a spatial distance between A and B. This spatial distance is real, and therefore not arbitrary.

A particle cannot be at position A and B at the same time

Let the particle be at position A at time C and be at position B at time D

There is a temporal duration between C and D. This temporal duration is also real, and therefore also not arbitrary.

That a particle cannot be at two different positions at the same time means that neither spatial distance nor temporal duration are arbitrary.

There is a temporal duration between C and D. This temporal duration is also real, and therefore also not arbitrary. — RussellA

As I explain, that duration is arbitrary, because C and D are arbitrary points in time. You assume moments in time, but there are no real moments. Therefore, you could have chosen the duration between C and E or C and F or an infinity of other choices. That makes the choice, which determines th e length of duration, arbitrary in an absolute sense.

The supposed object, the particle, is a real empirically observable object, therefore it's position cannot be arbitrarily chosen, there are real spatial parameters which limit the truth, and restrict the designation of location.

Do you see the difference? The length of the duration is the product of choice in an absolute sense, because the supposed "moments" which constitute C, when the object is at A, and also D, when the object is at B, are inserted by choice (seemingly randomly). On the other hand, the supposed position of the object is restricted by real observations, i.e. truth.

(ignoring any debate in quantum mechanics) — RussellA

Quantum mechanics is actually very relevant because your chosen object was "a particle". Notice, that in quantum physics, the position of the particle is restricted by the truth of observation (where it is emitted and where it is detected). However, there is time between emission and detection when the particle cannot be said to have a location. This is because spatial location is restricted in the way I described. However, since temporal duration is not restricted in this way, we can still affirm that there is temporal duration during which the particle cannot be located. The arbitrariness of the temporal duration allows that there is a time period when the particle has no location, or every possible location, or however you want to interpret the consequence of this arbitrariness.

As I explain, that duration is arbitrary...The length of the duration is the product of choice in an absolute sense — Metaphysician Undercover

I agree when you say "The supposed object, the particle, is a real empirically observable object"

This particle can only exist at one position at one time.

I also agree when you say " therefore it's position cannot be arbitrarily chosen, there are real spatial parameters which limit the truth, and restrict the designation of location". I agree that when observed, as this particle can only exist at one position, its position has not been arbitrarily chosen.

However, I don't understand why one cannot equally say "therefore it's time cannot be arbitrarily chosen, there are real temporal parameters which limit the truth, and restrict the designation of time". When observed, as this particle can only exist at one time, its time has not been arbitrarily chosen.

I still don't see the difference you are trying to explain, in that distance is not arbitrary yet duration is arbitrary.

The particle is observed at a position and at a time. Neither are arbitrarily chosen. The position is the position I observe it to be at, and the time is the time I observe it to be at. As I cannot arbitrarily change the position I observe the particle to be at, I cannot arbitrarily change the time I observe the particle to be at.

However, I don't understand why one cannot equally say "therefore it's time cannot be arbitrarily chosen, there are real temporal parameters which limit the truth, and restrict the designation of time". When observed, as this particle can only exist at one time, its time has not been arbitrarily chosen. — RussellA

What would those real temporal parameters consist of? If you think about it, they are all reducible to relative positions. So your starting point, t1, is completely arbitrary. You choose a specific position, and begin. The time itself has nothing within it to indicate to you what position is the starting position.

I still don't see the difference you are trying to explain, in that distance is not arbitrary yet duration is arbitrary. — RussellA

I don't know, maybe I'm the one who is wrong, who misunderstands. But you haven't been able to explain to me why what I'm saying doesn't jive with your belief, so we're both just not making sense to the other.

Neither are arbitrarily chosen. The position is the position I observe it to be at, and the time is the time I observe it to be at. — RussellA

I don't believe this, you choose (arbitrarily) what time to observe it. What, do you believe, restricts your choice of when to observe?

Einstein's theory of relativity has changed our conception of space, time and motion, but does not refer to whether space is continuous or not.
Therefore, Einstein’s theory of relativity, although forever changed our conception of space, time, and motion, still leaves the continuity of space untouched.

As the metaphysical reality of the Planck length is problematic, whether space is infinitely divisible or not, the same seems to apply also to time, whether time is infinitely divisible or not. — RussellA

No expert on the general theory of relativity or QM here but I think you will find the mathematics in GR does assume space is a continuous entity and that everything works well in the realm of the large but when one tries to apply GR to the smaller scales at which QM works the equations begin to give dubious (infinite) results. We currently work with 4 fundamental forces (strong nuclear, weak nuclear, EM and gravity). There are compatible mathematics for the first 3 which are essentially quantum (discrete not continuous and thus GR is the outlier. The most productive path for the TOE (theory of everything) or Universal Field Theory would seem to be some form of Quantum Gravity (loop, string, etc.) This would imply that neither time nor space are continuous but both would have some kind of discrete quantum formulation.
I am not sure philosophical discussions of time and space which precede our modern physics and which choose to ignore the seeming implications are relevant or reliable. There is no empty space. Space is a Dirac sea of virtual particles which appear and disappear on extremely short time scales. So the notion of empty space (devoid of matter) is purely an abstraction not a realty. There is clearly process and change in the universe (assuming we are not all brains in vat or being deceived by evil demons) but as for some universal fixed absolute time, there is no evidence. All our measures of time depend on some other process, the earth moving around the sun, the earths rotation of its axis, the sun rising and setting, the oscillations of watch spring, or vibrations of a quartz crystal or oscillations of cesium atoms and none of these are absolute all subject to the effects of acceleration or gravity (special relativity). So it would appear there is no absolute time, and time is an abstraction from change. No dimensionless points and no instants of zero duration.

What would those real temporal parameters consist of? If you think about it, they are all reducible to relative positions. So your starting point, t1, is completely arbitrary. You choose a specific position, and begin. The time itself has nothing within it to indicate to you what position is the starting position. — Metaphysician Undercover

I must be missing what you are saying.

As time is relative, space is relative.

As there is no absolute point in space, there is no absolute point in time.

Therefore, as any starting point in time is arbitrary, then any starting position in space must also be arbitrary.

I am not sure philosophical discussions of time and space which precede our modern physics and which choose to ignore the seeming implications are relevant or reliable. — prothero

I agree that philosophy should not ignore modern physics, but this is not necessarily the case with quantum mechanics, where there is still much disagreement.

After just a quick look on the internet:

Sabine Hossenfelder. Did We Get the Double Slit Experiment All Wrong?

Sabine Hossenfelder. Gamechange: Theories Of Everything Can’t Exist, Physicists Show.

Sabine Hossenfelder. Why This Nobel Prize Winner Thinks Quantum Mechanics is Nonsense

Sean Carroll. Even Physicists Don’t Understand Quantum Mechanics. Worse, they donʼt seem to want to understand it.

As you said yourself, the mathematics of General Relativity breaks down at smaller scales.

Philosophy should take into account modern physics, but not those parts of modern physics that remain contentious, such as quantum mechanics, where there is even disagreement amongst the physicists themselves.
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There is clearly process and change in the universe....................All our measures of time depend on some other process, the earth moving around the sun...........................So it would appear there is no absolute time, and time is an abstraction from change. — prothero

Putting what you say into premises and conclusion:

Premise 1 - there is change in the universe
Premise 2 - the measurement of time depends on change
Conclusion - time is change

Premise 2 is a definition, where time is defined as change.
Putting this definition into premise 1, there is time in the universe

The conclusion that time is change is more a premise than it is a conclusion.
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The most productive path for the TOE (theory of everything) or Universal Field Theory would seem to be some form of Quantum Gravity (loop, string, etc.)........................This would imply that neither time nor space are continuous but both would have some kind of discrete quantum formulation....................No dimensionless points and no instants of zero duration. — prothero

It may be that in the future there is a TOE, and even if there is, it may be that this implies that neither space not time are continuous but discrete.

However, so far, this is not the case, so does not tell us at the moment that there are no dimensionless points and no instants of zero duration.