hmmm...Zeno...I must refresh my memory of this guy....a beautiful mind comes to uhmmm mind! haQuantum Heraclitus:
First off, I am the one who loves Zeno. Not you. Stop ripping him off, or I will go Eleatic Stranger on your ass, Plato style.
Seriously. That's a promise, not a threat!
But what you have here is a somewhat faulty thought experiment to some extent.
The reason it is faulty is that an absence of time does not shrink the spatial properties. If something is 10 ly away, it will retain its 10 ly away, even if it is meaningless to speak of travel in a timeless state.
That is to say, distance is a spatial not a temporal property.
That being said, if it takes two moments (let moment = smallest increment of time) time to move from point a to point b, when point a and b are two arbitrary points in space, you have infinite speed. If no time is taken (impossible) the object would exist at two points simulteneously. But this is neither here nor there whatsoever and has no bearing on the thought experiment.
Any ways,
The object of this thread is to prove that distance exists independant of time. It is not good enough to rely on a possibly faulty space time description as per Minkowski/Einstein or any other.
I realise that according to current thought space and time are interrelated and to some extent I would agree but this has yet to be proved and only at present this is assumed to be the case. [ as all evidence seems to support the inter-relationship ]
Purely circumstancial evidence is not sufficient.
I would say that if one holds to the current view of spacetime there can be no distinction between space and time drawn. Distance is a factor of time...and vica versa ....end of story.
However I do not agree with the current view of space and time and wish that view be supported with appropriate proofs or at least understanding.
Does mass [ time ] create the distance? Thus does mass create 3 dimensions by default of the 4th?
If so then if no mass is present then what are the dimensions? Is there evidence to support the notion that a metre cube of pure vacuum is in fact a metre cube?
I would contend that a metre cube of pure vacuum only achieves dimensionality above zero simply because we would use an object of mass as a measuring device. Thus the device itself imparts dimensionality and can not tell us what the actual dimesnions are without corrupting what is being measured.
The answer in my opinion is that a metre cube of pure vacuum is actually zero dimensional when one stops applying a measurement of mass to it.
"Space is a volume of zero dimensionality that the universe exists within"
"It is a volume of space [area] that can be any size the mass requires"
And just because we have objects of mass doesn't change the nature of space as being zero dimensional unless vacant space has a means to achieve distance which is what we are attempting to prove.
How does vacant space acquire a structure to achieve distance when there is nothing there? It is not an aether. It has no qualities other than absense.
How does a bit of vacuum gain structure to qualify as a dimension?
and so on....