Re: Can gravity become infinitely small?

Dear curiosus_2008:

On Jan 15, 3:45 pm, curiosus_2...@xxxxxxxxx wrote:
David A. Smith wrote:
We can measure space with infinite precision, but it
will take infinite time to do so.  Which says nothing
about "accuracy"...

That is a consequence of the Heisenberg uncertainty
principle.

Perhaps.

I have two objections:

First we don't have an infinite time to make the
experiment, and we don't have the certainty that
time can become infinite.

Would not "fourteen significant figures" be enough, or would you
require and infinite number of sig figs to satisfy yourself that
"space is for all intents and purposes, continuous"?

Then, according to QM, the Planck length is the
smallest amount of length with significance, and
below this length all measurements are nonsense.

This is total bologna. Planck units are bogus, and do *NOT* derive
from QM. Do not hang your hat on a failed attempt at dimensional
analysis. Does "Planck mass" have any significance? No. Neither
does "Planck length".

...
It *must* be.  Because the slope across a step change is
infinite.  No such infinities show up.

In digital signal processing, we are working with step
changes.

What is is about *digitial* signal processing that makes you think
that the fact that signals are "binned" to nearby values, rather than
treated as analog values, has anything to do with the underlying
Nature being observed? The circuitry provides the "step" change...
the measured source does not (necessarily).

Basically, a sampled signal includes only step changes,
not smooth changes.

Circuitry driven step...

However we have no problems computing derivatives. Why?

Because there a step change both in time and space, so
there is a natural compensation.

How can you prove this? If you cannot, then you propose something
that can *never* be detected.

...
I agree that what underlies continuity is discrete.
 I disagree that such discreteness is detectable via
"space" or "time".  I submit that any measurement of
space or time (or mass) derive from the entire
Universe, so must yield a continuous result. Show
me I am wrong, don't just talk about it.

Planck's length and time limits prevent us from
computing or measuring a trajectory with an infinite
number of points, in space and in time.

These "magic numbers" provide no such limitation.

That is a consequence of both QM and GR:

"The following thought experiment illuminates this fact.
The task is to measure an object's position by bouncing
electromagnetic radiation, namely photons, off it. The
shorter the wavelength of the photons, and hence the
higher their energy, the more accurate the measurement.
If the photons are sufficiently energetic to make
possible a measurement more precise than a Planck length,
their collision with the object would, in principle,
create a minuscule black hole. This black hole would
"swallow" the photon and thereby make it impossible to
obtain a measurement. A simple calculation using
dimensional analysis suggests that this problem arises if
we attempt to measure an object's position with a
precision to within a Planck length."

(from http://en.wikipedia.org/wiki/Planck_length)

It is empty-headed bull***. By the way, do a search on:
"dual to a black hole"

To sum it up, we have this situation:

In the real world we cannot build or measure anything
fully continuous or smooth.

Can, and do. Just not with digital equipment.

...
That seems to be a paradox: mathematics seem to govern
the real world, but they cannot exist fully in it.

No paradox. Mathematics is the tool used to predict how Nature
behaves. She seems to be predictable in that way. I doubt Nautre
uses any sort of calculator.

My proposition, to solve that paradox, is to
postulate that mathematics exist really, but in
a parallel universe.

Show discreteness first. Then let me have a moving observer get the
same values you do. He won't. Discreteness occurs "below"
SpaceTimeMass.

David A. Smith
.

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