
Is space like a chessboard? - zoowar
http://www.physorg.com/news/2011-03-space-chessboard.html
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fuzzmeister
"Space is usually considered infinitely divisible — given any two positions,
there is always a position halfway between."

I'm unsure if this can be extended to space, but I know that current theories
state that there is a unit of time (the Planck time) that seems to be, in a
sense, indivisible:

"Within the framework of the laws of physics as we understand them today, for
times less than one Planck time apart, we can neither measure nor detect any
change."

<http://en.wikipedia.org/wiki/Planck_time>

Could someone more knowledgeable in physics than myself elaborate on whether
this fact would also mean that spacetime, and thus space, is "indivisible"?

~~~
rorrr
<http://en.wikipedia.org/wiki/Planck_length>

This seems more appropriate.

~~~
fuzzmeister
Yes, but I didn't post that because of this quote, which led to my overall
confusion: "The physical significance of the Planck length, if any, is not yet
known."

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VladRussian
>Electrons are thought to spin, even though they are pure point particles with
no surface that can possibly rotate.

for an article related to theoretical physics and QM this opening is as bald
as e2-e4. "Surface", "spin" [as in spinning wheel], "rotate" ?

Reading further:

>Space is usually considered infinitely divisible — given any two positions,
there is always a position halfway between.

considered by whom?

>If the electron had a radius, the implied surface would have to be moving
faster than the speed of light, violating the theory of relativity.

well, it wouldn't be the first time a QM effect wouldn't fit the SR. The SR is
applicable only between medium macro scale and medium micro scale [ and only
to the speeds equal or below "c" ] . Large macro scale is outside SR - during
last 13B years the Universe has expanded to the size much larger than 26B of
light years. And the "electron surface speed" [or whatever there may be
instead of the "surface", "speed", etc...] is well below the scale where SR is
still applicable.

The SR is about movement [and its "speed" as in "space"/"time" ] relative to
local space in the local time with both modeled as _mathematically_
continuous. At the very large macro scales - Universe and its time - the space
itself expands [ please don't mistake it for "observed" by SR "observer"
expansion/contraction of the fixed local space] . At the very micro scale -
the SR's models of the space and time aren't accurate enough to be used as a
foundation for any conclusions about that scale.

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Raphael
My physics teacher said that spin is not necessarily rotation, more of a
mathematical metaphor.

~~~
hansen
It actually can't be rotation, otherwise the magnetic moment of charged
particles comes out wrong by a factor two.

From the mathematicians point of view spin arises naturally when you study how
to represent the symmetries of special relativity. Quantum mechanics taught us
that a physical state is represented by something called the "wave function".
Different observers (e.g. one moving relatively to the other with constant
speed) see different "wave functions" representing the same state.

Studying all mathematically consistent possibilities of how to calculate what
one observer sees if you know what the other sees leads to the possibility of
particles with spin.

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pbhjpbhj
>discovering a new way to think about the structure of space

Enquiry into the quantisation of space is hardly new.

From <http://www.jstor.org/pss/187807>: "A solution of the Zeno paradoxes in
terms of a discrete space is usually rejected on the basis of an argument
formulated by Hermann Weyl, the so-called tile argument. This note shows that,
given a set of reasonable assumptions for a discrete geometry, the Weyl
argument does not apply. The crucial step is to stress the importance of the
nonzero width of a line. The Pythagorean theorem is shown to hold for
arbitrary right triangles."

<http://en.wikipedia.org/wiki/Xeno%27s_paradox>
<http://en.wikipedia.org/wiki/Hermann_Weyl> raised the "distance function
problem" in respect of space comprising discrete parts

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eyeforgotmyname
That was awful.

