Clark, list,
Yes, the question of measuring sub-Planckian phenomena involves more
nuances than I got into or understand, and, for example, phenomena at
sub-Planckian lengths are not completely inaccessible in principle if,
as in the famous example, a universe-sized collider could tell us about
them. I'm keeping the audience in mind, some of whom may know even less
physics than I do (which is also why I say some things that you already
know). Let's not lose sight of the fact that the average educated reader
would not have expected that one could show, without a cosmic collider
or some such science-fictional device, that space does not show
granularity or pixellation (which some theories of quantum gravity seem
to call for) above a length of the order of 8∕100,000,000 of the Planck
length, i.e., atmospheric neutrino speeds appear not to vary in the way
that the idea of such granularity predicts, at least down to that level
of resolution. So some more versions of quantum gravity (don't ask me
which ones) have been experimentally disfavored. So quantum gravity
theories are not 100% untestable in current practice. Now, as I
understand it, such granularity or pixellation, nature as a discrete
computer, etc., would create problems for the Lorentz symmetry (which is
continuous) and would tend to imply a preferred reference frame, and one
would need to fine-tune added factors to cancel the problems out.
(Peirce had reasons based, as far as I can tell, in the nature of
thought and in the nature of spontaneity a.k.a. absolute chance, for a
continuity of space, time, and law. At any rate, continuity is looking
pretty good now.) The generic principle of relativity (laws of motion
look the same in all inertial reference frames) leaves one with a binary
choice (again, as I understand it) between the Galilean symmetry and the
more constraining Lorentz symmetry (which unites space and time,
quantifying them in the same units), so it's not like some other
symmetry is going to come along and rescue the principle of relativity
in such dire discrete straits. But my real point is that if observations
of atmospheric neutrinos can tell us about spacetime at almost
science-fictionally sub-Planckian lengths, then tests of distinctive
predictions from string theory shouldn't seem an impossible dream.
Thanks for the links!
Best, Ben
On 12/12/2016 11:14 AM, Clark Goble wrote:
(Sorry somehow managed to send this to the old list number. Stupid
Apple Mail.)
On Dec 11, 2016, at 12:48 PM, Benjamin Udell <baud...@gmail.com
<mailto:baud...@gmail.com> > wrote:
According to Wikipedia, the Planck length is, in principle, within a
factor of 10, the shortest measurable length – and no theoretically
known improvement in measurement instruments could change that. But
some physicists have found that that's not quite as much of a barrier
as it may seem to be.
It ends up being a bit more complex than that. It really depends upon
the system in question and what you are measuring. There’s also the
debate about whether this is epistemological or “real” (although when
people use that term they mean traditional realism not Peirce’s
realism which tends to blur the distinction).
BTW - a better discussion of Planck length is probably stack exchange
which gets into many of the nuances (both physical and philosophical).
It’s almost always a better source than Wikipedia on these topics.
http://physics.stackexchange.com/questions/185939/is-the-planck-length-the-smallest-length-that-exists-in-the-universe-or-is-it-th
The short answer is that gravitational effects become dominate below
the Planck length we assume. Since we don’t have a theory of quantum
gravity this region is more or less ‘no man’s land’ unless one tries
to apply string theory or the like. Beyond that it’s just a scale
factor and we probably shouldn’t say much beyond that. (Again unless
one is doing theoretical work in quantum gravity - but that has its
own problems)
Typically in practical QM problems we assume a classical continuous
substantial spacetime and ignore all these issues. In that case we’re
just worried about what we can measure in principle about *that*
system from the math.
A few other useful ones:
http://physics.stackexchange.com/questions/9720/does-the-planck-scale-imply-that-spacetime-is-discrete
http://physics.stackexchange.com/questions/28720/how-to-get-planck-length
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
