A Penn State scientist studying crystal structures has developed a new mathematical formula that may solve a decades-old problem in understanding spacetime, the fabric of the universe proposed in Einstein’s theories of relativity.

“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,” said Venkatraman Gopalan, professor of materials science and engineering and physics at Penn State. “However, something about the time-axis sticks out like sore thumb.”

For calculations to work within relativity, scientists must insert a negative sign on time values that they do not have to place on space values. Physicists have learned to work with the negative values, but it means that spacetime cannot be dealt with using traditional Euclidean geometry and instead must be viewed with the more complex hyperbolic geometry.

Gopalan developed a two-step mathematical approach that allows the differences between space and time to be blurred, removing the negative sign problem and serving as a bridge between the two geometries.

“For more than 100 years, there has been an effort to put space and time on the same footing,” Gopalan said. “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.” The paper, published on May 27, 2021, in the journal *Acta Crystallographica A*, is accompanied by a commentary in which two physicists write that Gopalan’s approach may hold the key to unifying quantum mechanics and gravity, two foundational fields of physics that are yet to be fully unified.

“Gopalan’s idea of general relativistic spacetime crystals and how to obtain them is both powerful and broad,” said Martin Bojowald, professor of physics at Penn State. “This research, in part, presents a new approach to a problem in physics that has remained unresolved for decades.”

In addition to providing a new approach to relate spacetime to traditional geometry, the research has implications for developing new structures with exotic properties, known as spacetime crystals.

Crystals contain repeating arrangement of atoms, and in recent years scientists have explored the concept of time crystals, in which the state of a material changes and repeats in time as well, like a dance. However, time is disconnected from space in those formulations. The method developed by Gopalan would allow for a new class of spacetime crystals to be explored, where space and time can mix.

“These possibilities could usher in an entirely new class of metamaterials with exotic properties otherwise not available in nature, besides understanding the fundamental attributes of a number of dynamical systems,” said Avadh Saxena, a physicist at Los Alamos National Laboratory.

Gopalan’s method involves blending two separate observations of the same event. Blending occurs when two observers exchange time coordinates but keep their own space coordinates. With an additional mathematical step called renormalization, this leads to “renormalized blended spacetime.”

“Let’s say I am on the ground and you are flying on the space station, and we both observe an event like a comet fly by,” Gopalan said. “You make your measurement of when and where you saw it, and I make mine of the same event, and then we compare notes. I then adopt your time measurement as my own, but I retain my original space measurement of the comet. You in turn adopt my time measurement as your own, but retain your own space measurement of the comet. From a mathematical point of view, if we do this blending of our measurements, the annoying minus sign goes away.”

References:

“Relativistic spacetime crystals” by V. Gopalan, 27 May, *Acta Crystallographica A*.

DOI: 10.1107/S2053273321003259

“From crystal color symmetry to quantum spacetime” by M. Bojowald and A. Saxena, 27 May, *Acta Crystallographica A*.

DOI: 10.1107/S2053273321005234

The National Science Foundation funded this research.

The space-time crystàĺ is a practical pìece of matter,with usual 3-D of space can indìcaþe time dìmension aĺso.Here,gravityisthe propòrtý that does nòt change but reflects relativìstic effect.Now,the crystal has its own set of space coordinates and an extra coordinate of time,thate is indicated by some caliberated gauge of natural proporties of the materials of crystal.

The space-time crystàĺ is a practical pìece of matter,with usual 3-D of space can indìcaþe time dìmension aĺso.Here,gravityisthe propòrtý that does nòt change but reflects relativìstic effect.Now,the crystal has its own set of space coordinates and an extra coordinate of time,thate is indicated by some caliberated gauge of natural proporties of the materials of crystal.Often some rare crystal pieces formed by natùre show space-time propòrty to some limitations needed to be mòulded to get perfectness.

Hmm… There is an easy way to solve this with crystals… Instead of exchanging random arbitrary time stamps exchange coordinates and a count of a crystals vibrations at each of at least two coordinates. Time can then be normal and realized and unrenormalized.

This flys in the face of simplification and is not elegant. Isn’t the point of relativity to be a calculation of your place in space and time “relative” to light? Isn’t the – sign just a proxy for a second observation anyway? What is the point?

Não vamos nos esquecer que este método de Gopalan tende a simplificação como via de normatização de valores…resolve à questão da reflexividade de um eixo no espaço, mas provoca refração em seus functores de tempo…logo, tempo precisa que D seja reflexivo em sua funçao com C…sendo que os Múons estão decaindo em Nitritos, somente D sendo cofunctor em G será possível nova dimensão do tempo pra C:D onde hadrons cindem…

My girlfriend has one of these pink crystals next to her bed. Super cool.

COULD BE TRIANGULUS STAR FORMATION. …..NEGATIVE TIME THE PAST OF THE FUTURE AND SOME PRESENT. PREVENTING FUTURE DESASTERS!

Forgive me, but are there any theories that matter and the forces are actually all manifestations of space time…https://hmmphty.wordpress.com/2010/11/01/zero-energy-theory/

I’m just over here wondering what color lightsaber these space crystals will create and when do I get mine?

…

The first of all, it said: “three space-axes and one time-axis”. So, we can go back in time now? I didn’t know that.Then one can complain about weird solutions that make no sense…

… that is not the best one, that is what you get for difference at quantum level…

…”You make your measurement of when and where you saw it, and I make mine of the same event, and then we compare notes. I then adopt your time measurement as my own, but I retain my original space measurement of the comet. You in turn adopt my time measurement as your own, but retain your own space measurement of the comet. From a mathematical point of view, if we do this blending of our measurements, the annoying minus sign goes away.”…

… okay, you take mess and make it even messier, or you hope that odd parts will cancel each other… that might be a good path, but…

This is all fine. Aren’t time and space the same thing? Any distance requires time to cross. But my problem is the whole entire premise of how we got here is the bs part. Explain to me how nothing escapes a black hole but yet here we are. You can’t have both. But lets say we did escape a black hole or singularity, how fast would we of had to be going to escape one. It had to be faster than the speed of light. But also isn’t a singularity infinite density and heat and mass? So to escape we had to be heavier than infinite. Or be moving at an unbelievable speed. We have the bad habit of moving forward without solving major flaws in the system first. Galaxies started to form how soon afterwards? But here is the real issue. If we slowed down, cooled down enough to form stars how did we accelerate again at an increasing rate ? But there is no way stars would form that soon and we would still be hauling ass. We can travel faster than light if the big bang is true. Anyway to many holes. Figure out the basic problems first. We came from God. Not nothing or a black hole. We were created. The evolution theory is gatbage and should not be taught in any school. Not one fossil has ever shown proof of the theory. A bird will always be a bird. Maybe a bigger and faster bird but always a bird. Mother nature does not allow freak shows. We need to start from scratch with some truths sprinkled in. And we didn’t come from nothing. Or there would be nothing. Explain nothing. Its impossible. Like explaining love. God bless

Why not get rid of time all together? Isn’t time just our perception of change in motion? If the comet wasn’t moving what difference could either person notice? You would have perceived the same event but you wouldn’t be able to tell the difference in perseption of time between the two people because the results would be the same.

Time is relative but what if so is space?