# [FOM] Question on the number line

Robert Lindauer rlindauer at gmail.com
Fri Nov 18 05:10:34 EST 2005

```Robert:

Say a given particle has two possible positions a-b.  At every time,
then, it is either in a or b.  Now consider an event, a switch from
state a to state b.  At every time it is in either a or b, it is never
in-between and never in both.  Presumably, if time is continuous and
the change from state a and state b is continuous in time (e.g. there
is no time at which the particle just disappears!), there is a time T -
presumably around the half-way time between it's being in state a and
state b, at which one needs to give an account of its rotational state.
But doing so is impossible since we've stipulated that it's either in
state a or b at any time.

The problem is just like the suarez problem in that faith in the
mid-point of the change in state creates a paradox of the state of the
particle at the time in question.  The correct response is, I think, to
reject the idea that there is any such time.  The particle is always in
either A or B, and one ought to conclude that time therefore is
discontinuous or at least that the particle is discontinuous in time
(making the notion of continuous time superfluous).

On Nov 17, 2005, at 12:27 AM, Robert Black wrote:

>  an
> explanation of how things like quantum mechanics and general
> relativity should be reformulated to fit in with the new topology,
> and I doubt if anyone is claiming that they can do this (or that some
> scholastic or Aristotelian argument forces us to do it).

I think it is understood that the mathematics supporting quantum
mechanics anyway could be formulated on a purely integral basis
locating all particles on a very fine integral grid in four dimensions.

All physical units can be expressed as a combination of planck's
constant, the speed of light and the universal gravitation constant.
The finest time required for actually describing any real particles is
more than 10^-44 seconds which we could use as a base for the
(integral) grid if required to do so.  If we wanted to be CERTAIN, we
could use 10^-1024 seconds as our basic time-unit and 10^-1024 mm as
the basic space-unit.  We have very good experimental evidence that
tells us that measurements of interactions with values less than these
will be fabrications and that measurements at the level of planck's
distance constitute the smallest DETECTABLE space component given that
we must interact with the measured objects using photons.

That would be adequate for a description of any state of particles
found therein.  Any further discussion of particle-reactions and
relations less than that distance are meaningless in QM, anyway.  So I
would put the matter quite the other way - the current QM topology is
integer-based.  The fictitious continuous-topology-QM theory needs to
be explicated more fully.

Best,

Robbie Lindauer

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