Re: Space-Time, mathematics and physics

On Jul 30, 10:52 am, Jean Paul <jcorriv...@xxxxxxx> wrote:
Hello.

[...]
But the set of coordinates (r, t) represent a *trajectory* of some
radiation (or whatever it is) in the Space-Time dimensions. In the
case of particules, I deducted by myself that their trajectory is
discrete. So then this formula reflects a discrete function,
suggesting that Space and Time dimensions are discrete. Again that
formula expresses the trajectory of a particle, or radiation, or
whatever. The formula does *not* imply anything about the *nature* of
the Time and Space dimensions. If the trajectory is discrete, does
that imply that the dimensions are discrete too? That is my big
question to you all, and the answer does not seem so immediate.

I have to admit that a continuous dimension appears to be an
impossibility in the physical world, if we assume the definition of
continuity from mathematics. So this suggests that all dimensions are
discrete. But philosophically, I find this extremely difficult to
grasp.

Maybe we should not view particles travelling in Space-Time, but
rather view something less tangible like energy, waves... travelling
in space? If we refer to particles jumping around in discrete steps,
then it appears impossible to avoid the question of what is in between
those steps? This is my dilemma.

If anyone can help me, I would be grateful. I know that it would help
if I knew more about physics. All I learned in college is one course,
the classical Newton's mechanics. Is it at all possible to make me
understand without me having to take a BSc in Physics? I'm too busy to
take courses toward a BSc.

Thank you.

The dilemma you refer to is interesting and, I think,
important. I also got into a struggle with it, in the past,
so I will give you what I think is able to answer it.

Firstly, every measurable reality, such as distance in space
or time, must, unavoidably, be discretised, or quantised,
because there must always be a basic, finite quantum that
exists as the unit of the measure. You cannot have a measure
based on continuity, because then you have a measure made
up of an infinite number of units of zero size, which is nonsense.

I believe this consideration applies not only to artificial units of
measurement invented by scientists, but also in nature itself.
It makes sense to suppose that, if reality can be described only
in terms of such artificial measurement, it also exists in terms of
its own, equivalent, natural measurements. Thus, such realities
must be actually discrete, which is in accordance with quantum
theory.

But what, then, of continuity?

I believe that continuity also exists, in the following way: If you
conceive a finite quantum as the discrete unit of a measure,
in a particular physics, it is obvious that you could also
conceive that there could be another physics in which the
quantum of the measure could be smaller, and yet another, in
which it could be smaller still, and so on, ad infinitum. This means,
immediately, that a discrete reality automatically also displays
the potential to be discretised in endlessly different possible ways,
and it is really this potential, which really exists, that is referred
to by the term 'continuity'. Thus, continuity is the potential for
the quantum of a measure to be endlessly smaller while, at the
same time, the measure must always be actually discretised in
a particular way.

A reality must thus be both discrete and continuous at the
same time. According to its existence, as such, a reality is
continuous but, in the measure by which it is manifest as
measured, it is discrete. An object thus does not intrinsically
move in discrete jumps, but the measure of its movement,
not the movement itself, must display discrete jumps, which
are units of measurement selected out of an endless series
of different possible units of measurement. Any one of these
could potentially be applied within a reality, in virtue of its
intrinsic continuity.

Alen

.

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