Re: Continuity of spacetime

If the distance from 0 to 1 on [ 0, 1 ] is really
equal to say .5,
because the probability of the exitence of any given
x_n is 50:50, then
you might as well be talking about the interval [ 0,
.5 ] where the
probability of existence of any given x_n is %100.
These things seem
interchangeable, indeterminately so, and so the whole
approach might
rightly be characterized as being trivial.

The closed interval [a,b] as I wrongly expected you
to understand from the link I gave, contains all of
its limit points.

Correct.

If you know what that means, then
you should see that the existence question you pose
is not an issue.

And what I am saying is that energy is nothing more than an existential
probability gradient, and that this is the correct wave-based approach
to QM.

The word energy has been obsoleted. Everything can be described in
terms of probailities.


If it is the dichotomy between
the continuous line and discrete numbers that troubles
you --

Nope - I dont even think that what I said could be read that way.


Dedekind handled it with a cut principle that
straightforwardly instructs us in how to differentiate
real numbers without sacrificing continuity.

Other than that, as a couple of us have pointed out, you
are confusing physical measurability with mathematical
models. Two different things.

Tom


No. I'm giving the reals a new property, just to see what happens. The
property which you assign to each real is a real valued probability on
[0,1] that the point in question exists. An "existential potential".
Length is then derived with a combination of metric and an associated
PD.

In empty flat space, the PD would be everywhere near 1. On quantum
scale you can have that the PD is closer to being everywhere near 0,
and so you get paths of zero distance.

The measurement problem is entirely different. I'm saying that length
is "everywhere probailistic", no particles needed in this approach
whatsoever.


Again, the problem with an approach based on triviality is that the
validity of the approach is always indeterminate, regardless of how
well experiment agrees with theory, even if it matches up perfectly,
validity will always be indeterminate.

.

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