New Approach Relates Spacetime Crystals to Traditional Geometry

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May 28 2021

专注于晶体结构，一名研究员宾夕法尼亚州立大学（Penn State) has designed a novel mathematical formula that might solve an ancient issue in interpreting spacetime—the foundationof the universe suggested in Albert Einstein’s theories of relativity.

展示创建“重新运识化混合时空”的过程的图。宾夕法尼亚州科学家Venkatraman Gopalan正在研究水晶结构，并开发了一种新的数学公式，可以解决在理解时空，宇宙中所提出的相对论理论的宇宙的织物中的十年历史问题。图片学分：Hari Padmanabhan，Penn State。

Relativity tells us space and time can mix to form a single entity called spacetime, which is four-dimensional: three space-axes and one time-axis。However, something about the time-axis sticks out like sore thumb。

Venkatraman Gopalan，宾夕法尼亚州立大学材料科学与欧洲杯足球竞彩工程教授欧洲杯线上买球

为确保计算在相对论中工作，研究人员首先需要在时间值上引入负符号，这不必放置在空间值上。虽然物理学家已经了解了使用负值的概念，但它还意味着不能用传统的欧几里德几何来解决空间，而是应该使用更复杂的双曲几何形状可视化。

Gopalan设计了两步的数学策略，有助于模糊时间和空间之间的变化，从而消除了负符号的问题，并作为两个几何形状之间的桥梁。

For more than 100 years, there has been an effort to put space and time on the same footing. But that has really not happened because of this minus sign. This research removes that problem at least in special relativity. Space and time are truly on the same footing in this work。

Venkatraman Gopalan，宾夕法尼亚州立大学材料科学与欧洲杯足球竞彩工程教授欧洲杯线上买球

Recently published in theActa Crystallographica Ajournal on May 27^TH., 2021, the article is accompanied by a commentary where a couple of physicists have cited that Gopalan’s mathematical approach may provide the solution to combine gravity and quantum mechanics—two fundamental areas of physics that have not been completely unified yet.

“Gopalan’s idea of general relativistic spacetime crystals and how to obtain them is both powerful and broad. This research, in part, presents a new approach to a problem in physics that has remained unresolved for decades，“宾夕法尼亚州的物理学教授”Martin Bojowald“。

除了提供全新的方法来与常规几何形状相关的全新方法，新的研究对设计具有不同寻常性质的新型结构的影响，称为空间晶体。

In crystals, atoms are arranged in a repeated pattern, and in the recent past, scientists have investigated the theory of time crystals, where the state of a material alters and also repeats in time, similar to a dance.

但是时间从这种配方中的空间删除。Gopalan的方法将有助于探索一系列新的空间晶体，其中时间和空间可以组合在一起。

除了了解许多动态系统的基本属性之外，这些可能性可以迎来一个完全新的超大属性，否则无法获得异国特性，否则无法获得若干动力系统的基本欧洲杯足球竞彩属性。

Avadh Saxena, Physicist, Los Alamos National Laboratory

The technique devised by Gopalan involves combining a couple of individual observations of the same event. Blending takes place when a couple of observers exchange time coordinates but still maintain their own space coordinates. With renormalization—an extra mathematical step—this results in “renormalized blended spacetime.”

“让我们说我在地上，你在空间站飞行，我们都观察了像彗星飞行的活动。你可以测量你看到它的时间和地点，我制作了相同的事件，然后我们比较笔记。然后我作为自己的时间测量，但我保留了我的原始空间测量彗星，“加上戈帕兰。

“您反过来采用我的时间测量为自己的，但保留自己的彗星空间测量。从数学的角度来看，如果我们这样做的测量混合，令人讨厌的减号消失了,” concluded Gopalan.

该研究由国家科学基金会资助。欧洲杯线上买球