[FOM] Question on the number line

[Robert Lindauer]

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