5 ms·

Is space like a chessboard?

17 points by zoowar 16y ago

deleted 16y ago
[deleted]
VladRussian 16y ago
>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.
fuzzmeister 16y ago
"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 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 16y ago
  http://en.wikipedia.org/wiki/Planck_length http://en.wikipedia.org/wiki/Planck_length This seems more appropriate.
  - fuzzmeister 16y ago
    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."
- ionfish 16y ago
  According to general relativity, spacetime is a smooth continuum. However, due to issues arising from quantum mechanics, some have proposed that spacetime should be quantised. http://en.wikipedia.org/wiki/Quantum_spacetime http://en.wikipedia.org/wiki/Quantum_spacetime
eyeforgotmyname 16y ago
That was awful.
Raphael 16y ago
My physics teacher said that spin is not necessarily rotation, more of a mathematical metaphor.
- hansen 16y ago
  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.
- pbhjpbhj 16y ago
  Spin refers to both intrinsic spin angular momentum and orbital angular momentum, http://books.google.com/books?id=3_7uriPX028C&lpg=PA31&pg=PA80#v=onepage&q=spin&f=false http://books.google.com/books?id=3_7uriPX028C&lpg=PA31&#.... I think of intrinsic spin in part as being an ability to impart an angular momentum (magnets, how do they work!?), though I'm not sure how well that really works in practise it's just my mental model. Also it's interesting to speculate about charge-spin separation in electrons (spinons, holons). I have a pet (completely unworked) hypothesis that spin somehow exists across dimensions we experience and other dimensions - that the property could be a coupling with a "spining" (or spin) particle in a dimension outside Minkowski spacetime.
pbhjpbhj 16y ago
>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 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/Xeno%27s_paradox http://en.wikipedia.org/wiki/Hermann_Weyl http://en.wikipedia.org/wiki/Hermann_Weyl raised the "distance function problem" in respect of space comprising discrete parts

17 points by zoowar 16y ago

deleted 16y ago

[deleted]

>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.

fuzzmeister 16y ago

"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 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 16y ago
http://en.wikipedia.org/wiki/Planck_length http://en.wikipedia.org/wiki/Planck_length This seems more appropriate.
- fuzzmeister 16y ago
  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."
ionfish 16y ago
According to general relativity, spacetime is a smooth continuum. However, due to issues arising from quantum mechanics, some have proposed that spacetime should be quantised. http://en.wikipedia.org/wiki/Quantum_spacetime http://en.wikipedia.org/wiki/Quantum_spacetime

eyeforgotmyname 16y ago

That was awful.

Raphael 16y ago

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

hansen 16y ago
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.
pbhjpbhj 16y ago
Spin refers to both intrinsic spin angular momentum and orbital angular momentum, http://books.google.com/books?id=3_7uriPX028C&lpg=PA31&pg=PA80#v=onepage&q=spin&f=false http://books.google.com/books?id=3_7uriPX028C&lpg=PA31&#.... I think of intrinsic spin in part as being an ability to impart an angular momentum (magnets, how do they work!?), though I'm not sure how well that really works in practise it's just my mental model. Also it's interesting to speculate about charge-spin separation in electrons (spinons, holons). I have a pet (completely unworked) hypothesis that spin somehow exists across dimensions we experience and other dimensions - that the property could be a coupling with a "spining" (or spin) particle in a dimension outside Minkowski spacetime.

pbhjpbhj 16y ago

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