[math-fun] quantum entangled clock network? Ultra-accurate?
I'm unsure whether this idea is completely insane: https://www.sciencenews.org/article/quantum-timekeeping
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process.. On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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Just to add - attractors classified as "Cantor dust" do not solely consist of collections of zero-dimensional points like the Cantor Set, Cantor Dust attractors include those consisting of separate parts each of which can be of any dimensionality. On 25 Feb 2014, at 23:00, David Makin wrote:
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process..
On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set. On Tue, Feb 25, 2014 at 6:08 PM, David Makin <makinmagic@tiscali.co.uk>wrote:
Just to add - attractors classified as "Cantor dust" do not solely consist of collections of zero-dimensional points like the Cantor Set, Cantor Dust attractors include those consisting of separate parts each of which can be of any dimensionality.
On 25 Feb 2014, at 23:00, David Makin wrote:
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process..
On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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Funny thing --- despite being determinedly sceptical concerning claims of functioning quantum-theoretical cryptographic and computational devices, I somehow find the quantum super-clock sounds eminently practicable. Anyone else care to comment? WFL On 2/26/14, Allan Wechsler <acwacw@gmail.com> wrote:
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set.
On Tue, Feb 25, 2014 at 6:08 PM, David Makin <makinmagic@tiscali.co.uk>wrote:
Just to add - attractors classified as "Cantor dust" do not solely consist of collections of zero-dimensional points like the Cantor Set, Cantor Dust attractors include those consisting of separate parts each of which can be of any dimensionality.
On 25 Feb 2014, at 23:00, David Makin wrote:
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process..
On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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On 2/25/2014 5:15 PM, Fred Lunnon wrote:
Funny thing --- despite being determinedly sceptical concerning claims of functioning quantum-theoretical cryptographic and computational devices, I somehow find the quantum super-clock sounds eminently practicable. Anyone else care to comment? WFL
Sounds fascinating. Note that parts of the entangled superclock located at different latitudes on the Earth will be keeping different sidereal times. This is because the Earth's surface is (roughly) at constant gravitational potential so the GR effect will be the same at different latitudes, but the special relativistic effect will be greater nearer the equator. So, relative to sidereal time, the equatorial parts will run slower than the polar parts. I think this just shows there's no consistent way to define simultaneity on a rotating frame - but I'm not sure. Brent Meeker
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point
Sorry, I left out the word "disconnected" (spatially not functionally) and although you're correct about the non-isolated nature of the Cantor Set itself, that doesn't apply to the full generalisation of Cantor Dusts and certainly not to non-infinite dusts (i.e. with a finite number of separate disconnected parts). On 26 Feb 2014, at 00:01, Allan Wechsler wrote:
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set.
On Tue, Feb 25, 2014 at 6:08 PM, David Makin <makinmagic@tiscali.co.uk>wrote:
Just to add - attractors classified as "Cantor dust" do not solely consist of collections of zero-dimensional points like the Cantor Set, Cantor Dust attractors include those consisting of separate parts each of which can be of any dimensionality.
On 25 Feb 2014, at 23:00, David Makin wrote:
Consider quantum entanglement in terms of disconnected attractors - a form of Cantor Dust, - so even though physically distant they are still part of a single mathematical function/system/process..
On 25 Feb 2014, at 22:30, Warren D Smith wrote:
I'm unsure whether this idea is completely insane:
https://www.sciencenews.org/article/quantum-timekeeping
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
To a topologist, all Cantor sets are, by definition, homeomorphic to the archetypal middle-third one, and so to each other. Two points of a topological space are said to be in the same connected component if there do not exist two disjoint open sets, each containing one of the two points. From this definition it’s easy to check that the connected components of the (any) Cantor set are its individual points. Hence the Cantor set is called “totally disconnected”. As Allan points out, every point of the Cantor set is a limit point of the set, i.e., no point is isolated. Yet this is consistent with its being totally disconnected. —Dan On Feb 25, 2014, at 4:01 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set.
Very slight edit inserted in Dan's explanation, which I'm pretty sure he'll agree with: On Tue, Feb 25, 2014 at 10:28 PM, Dan Asimov <dasimov@earthlink.net> wrote:
To a topologist, all Cantor sets are, by definition, homeomorphic to the archetypal middle-third one, and so to each other.
Two points of a topological space are said to be in the same connected component if there do not exist two disjoint open sets
... *whose union is the whole space *...
each containing one of the two points.
From this definition it's easy to check that the connected components of the (any) Cantor set are its individual points. Hence the Cantor set is called "totally disconnected".
As Allan points out, every point of the Cantor set is a limit point of the set, i.e., no point is isolated. Yet this is consistent with its being totally disconnected.
--Dan
On Feb 25, 2014, at 4:01 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I'm not even sure if the archetypical Cantor set should be described as a "collection of zero-dimensional points", except in the sense that *every * point set is such a collection. No element of the Cantor set is isolated, in the sense that every neighborhood of a point in the Cantor set also contains other points in the set.
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participants (6)
-
Allan Wechsler -
Dan Asimov -
David Makin -
Fred Lunnon -
meekerdb -
Warren D Smith