提问人：星星点个灯。 发布日期：2022-09-23 11:40:29 浏览：393
摸着石头过河 发表于 2022-09-23 12:04:48
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热情。 发表于 2022-09-23 11:57:33
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小草 发表于 2022-09-23 11:59:27
理论物理的前沿E一Fractal logic space 从单一光子研究出发，看看原文吧
The Menger-Urysohn dimension is a generalized topological dimension of topological spaces, arrived at by mathematical induction. It is based on the observation that, in n-dimensional Euclidean space Rn, (n−1)-dimensional spheres (that is, the boundaries of n-dimensional balls) have dimension n−1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets.
The Hausdorff dimension generalizes the notion of dimension to irregular sets such as fractals. For example, a Cantor set has a Hausdorff dimension of ln2/ln3, the ratio of the logarithm to the base 2 of the parts remaining to the whole after each iteration.
A fractal is a mathematical set that typically displays self-similar patterns, and has fractional dimensions instead of the usual integer, 1, 2, 3, or 4. Geometric examples are branching trees, blood vessels, frond leaves etc.
The study of dynamical systems with locally unpredictable behaviour that is highly sensitive to initial conditions, but are nevertheless globally determined, such that the trajectories are confined within a region of phase space called ‘strange attractors’.
A term coined by Cantor; it means beyond finite, but not necessarily the absolute infinite.
E infinity fractal spacetime looks and feels 4-dimensional
The idea that spacetime is fractal originated with Canadian mathematician Garnet Ord  who coined the term ‘fractal spacetime’, using a model in which particles are confined to move on fractal trajectories.Independently, French astrophysicist Laurent Nottale proposed a scale-relativity theory of fractal spacetime . As Ord reminds us , American quantum physicist Richard Feynman (1918-1988) had already pointed out  that the paths of quantum mechanical particles look more like non-differentiable curves than straight lines when examined on a fine scale.
It is Egyptian-born Mohamed El Naschie, however, who has taken us furthest towards a coherent theory of physical reality that is also closest to our intuitive notion of organic spacetime. For precisely the same reasons, perhaps, El Naschie has attracted admiration and antagonism in equal measure.
As an aside, the journal Nature initiated a smear campaign against El Naschie in 2008 with an article written by its German correspondent  that was filled with insinuations and innuendoes, if not outright lies.It accuses El Naschie of “self-publishing” papers of “poor quality” without proper peer review in a theoretical physics journal of which he has been editor-in-chief. In fact, El Naschie has had hundreds of papers published in other journals; and his prolific output continued throughout the subsequent four-year period during which he brought a libel case single-handedly against Nature. El Naschie turned down all attempts by Nature to settle out of court, until the court ruled against him in 2012. By this time, Nature had spent £5 million in legal fees to defend itself. Given Nature’s shameful record in libeling myself and other scientists over the hazards of genetic modification, I became all the more determined to find out about El Naschie’s work; and have been suitably rewarded as a result.
El Naschie trained and practiced as an engineer while indulging in his hobby of cosmology, and produced a startling new theory of spacetime, which soon took over his life entirely. E-infinity, as he calls it, is a fractal spacetime with infinite dimensions. Yet its Hausdorff (fractal dimension) is 4.236067977... In other words, at ordinary resolution, it looks and feels 4 dimensional (three of space and one of time), with the rest of the dimensions ‘compacted’ in the remaining 0.236067977… “fuzzy tail”.
Think of a four dimensional hypercube with further four dimensional hypercubes nested inside like Russian dolls . In fact, the exact Hausdorff dimension is 4 + f3, where f = (√5-1)/2, the golden ratio.Particularly suggestive is that the dimension 4 + f3 show the following self-similar continued fraction (see Figure 1) which sums to precisely 4 + f3 at infinity:
The 4-dimensional hypercube is the Euclidean representation of the E-infinity universe. It is a challenge to represent E-infinity it in its proper non-Euclidean form.
吮硒坦鞋赞烷裔 发表于 2022-09-23 11:59:42
EL PSY CONGROO!!!
原弥 发表于 2022-09-23 12:01:51
El condor pasa 纯音乐！
西瓜西瓜 发表于 2022-09-23 12:02:10
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J chen 发表于 2022-09-23 12:05:31