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Three time dimensions, one space dimension: Relativity of superluminal observers in 1+3 spacetime

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Credit: Pixabay/CC0 Public Domain

How would our world be viewed by observers moving faster than light in a vacuum? Such a picture would be clearly different from what we encounter every day. “We should expect to see not only phenomena that happen spontaneously, without a deterministic cause, but also particles traveling simultaneously along multiple paths,” argue theorists from universities in Warsaw and Oxford.

Also the very concept of time would be completely transformed—a superluminal world would have to be characterized with three time dimensions and one spatial dimension and it would have to be described in the familiar language of field theory. It turns out that the presence of such superluminal observers does not lead to anything logically inconsistent, moreover, it is quite possible that superluminal objects really exist.

In the early 20th century, Albert Einstein completely redefined the way we perceive time and space. Three-dimensional space gained a fourth dimension—time, and the concepts of time and space, so far separate, began to be treated as a whole. “In the special theory of relativity formulated in 1905 by Albert Einstein, time and space differ only in the sign in some of the equations,” explains prof. Andrzej Dragan, physicist from the Faculty of Physics of the University of Warsaw and Center for Quantum Technologies of the National University of Singapore.

Einstein based his special theory of relativity on two assumptions: Galileo’s principle of relativity and the constancy of the speed of light. As Andrzej Dragan argues, the first principle is crucial, which assumes that in every inertial system the are the same, and all inertial observers are equal. “Typically, this principle applies to observers who are moving relative to each other at speeds less than the speed of light (c). However, there is no fundamental reason why observers moving in relation to the described physical systems with speeds greater than the speed of light should not be subject to it,” argues Dragan.

What happens when we assume—at least theoretically—that the world could be observable from superluminal frames of reference? There is a chance that this would allow the incorporation of the basic principles of quantum mechanics into the . This revolutionary hypothesis of prof. Andrzej Dragan and prof. Artur Ekert from the University of Oxford presented for the first time in the article “Quantum principle of relativity” published two years ago in the New Journal of Physics.

There they considered the simplified case of both families of observers in a space-time consisting of two dimensions: one spatial and one time dimension. In their latest publication in the journal Classical and Quantum Gravity, titled “Relativity of superluminal observers in 1 + 3 spacetime”, a group of 5 physicists goes a step further, presenting conclusions about the full four-dimensional spacetime.

The authors start from the concept of space-time corresponding to our physical reality: with three spatial dimensions and one time dimension. However, from the point of view of the superluminal observer, only one dimension of this world retains a spatial character, the one along which the can move.

“The other three dimensions are time dimensions,” explains prof. Andrzej Dragan. “From the point of view of such an observer, the particle ‘ages’ independently in each of the three times. But from our perspective—illuminated bread eaters—it looks like a simultaneous movement in all directions of space, i.e. the propagation of a quantum-mechanical spherical wave associated with a particle,” comments prof. Krzysztof Turzyński, co-author of the paper.

It is, as explained by prof. Andrzej Dragan, in accordance with Huygens’ principle formulated in the 18th century, according to which every point reached by a wave becomes the source of a new spherical wave. This principle initially applied only to the light wave, but extended this principle to all other forms of matter.

As the authors of the publication prove, the inclusion of superluminal observers in the description requires the creation of a new definition of velocity and kinematics. “This new definition preserves Einstein’s postulate of constancy of the speed of light in vacuum even for superluminal observers,” prove the authors of the paper. “Therefore, our extended special relativity does not seem like a particularly extravagant idea,” adds Dragan.

How does the description of the world to which we introduce superluminal observers change? After taking into account superluminal solutions, the world becomes nondeterministic, particles—instead of one at a time—begin to move along many trajectories at once, in accordance with the quantum principle of superposition.

“For a superluminal observer, the classical Newtonian point particle ceases to make sense, and the field becomes the only quantity that can be used to describe the physical world,” notes Andrzej Dragan. “Until recently it was generally believed that postulates underlying quantum theory are fundamental and cannot be derived from anything more basic. In this work we showed that the justification of quantum theory using extended relativity, can be naturally generalized to 1 + 3 spacetime and such an extension leads to conclusions postulated by quantum field theory,” write the authors of the publication.

All particles therefore seem to have extraordinary properties in the extended special relativity. Does it work the other way around? Can we detect particles that are normal for superluminal observers, i.e. particles moving relative to us at superluminal speeds?

“It’s not that simple,” says prof. Krzysztof Turzyński. “The mere experimental discovery of a new fundamental particle is a feat worthy of the Nobel Prize and feasible in a large research team using the latest experimental techniques. However, we hope to apply our results to a better understanding of the phenomenon of spontaneous symmetry breaking associated with the mass of the Higgs particle and other particles in the Standard Model, especially in the early universe.”

Andrzej Dragan adds that the crucial ingredient of any spontaneous symmetry breaking mechanism is a tachyonic field. It seems that superluminal phenomena may play a key role in the Higgs mechanism.

More information:
Andrzej Dragan et al, Relativity of superluminal observers in 1+3 spacetime, Classical and Quantum Gravity (2022). DOI: 10.1088/1361-6382/acad60

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University of Warsaw

 

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Three time dimensions, one space dimension: Relativity of superluminal observers in 1+3 spacetime (2022, December 22)
retrieved 22 December 2022
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Here’s how Helene and other storms dumped a whopping 40 trillion gallons of rain on the South

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More than 40 trillion gallons of rain drenched the Southeast United States in the last week from Hurricane Helene and a run-of-the-mill rainstorm that sloshed in ahead of it — an unheard of amount of water that has stunned experts.

That’s enough to fill the Dallas Cowboys’ stadium 51,000 times, or Lake Tahoe just once. If it was concentrated just on the state of North Carolina that much water would be 3.5 feet deep (more than 1 meter). It’s enough to fill more than 60 million Olympic-size swimming pools.

“That’s an astronomical amount of precipitation,” said Ed Clark, head of the National Oceanic and Atmospheric Administration’s National Water Center in Tuscaloosa, Alabama. “I have not seen something in my 25 years of working at the weather service that is this geographically large of an extent and the sheer volume of water that fell from the sky.”

The flood damage from the rain is apocalyptic, meteorologists said. More than 100 people are dead, according to officials.

Private meteorologist Ryan Maue, a former NOAA chief scientist, calculated the amount of rain, using precipitation measurements made in 2.5-mile-by-2.5 mile grids as measured by satellites and ground observations. He came up with 40 trillion gallons through Sunday for the eastern United States, with 20 trillion gallons of that hitting just Georgia, Tennessee, the Carolinas and Florida from Hurricane Helene.

Clark did the calculations independently and said the 40 trillion gallon figure (151 trillion liters) is about right and, if anything, conservative. Maue said maybe 1 to 2 trillion more gallons of rain had fallen, much if it in Virginia, since his calculations.

Clark, who spends much of his work on issues of shrinking western water supplies, said to put the amount of rain in perspective, it’s more than twice the combined amount of water stored by two key Colorado River basin reservoirs: Lake Powell and Lake Mead.

Several meteorologists said this was a combination of two, maybe three storm systems. Before Helene struck, rain had fallen heavily for days because a low pressure system had “cut off” from the jet stream — which moves weather systems along west to east — and stalled over the Southeast. That funneled plenty of warm water from the Gulf of Mexico. And a storm that fell just short of named status parked along North Carolina’s Atlantic coast, dumping as much as 20 inches of rain, said North Carolina state climatologist Kathie Dello.

Then add Helene, one of the largest storms in the last couple decades and one that held plenty of rain because it was young and moved fast before it hit the Appalachians, said University of Albany hurricane expert Kristen Corbosiero.

“It was not just a perfect storm, but it was a combination of multiple storms that that led to the enormous amount of rain,” Maue said. “That collected at high elevation, we’re talking 3,000 to 6000 feet. And when you drop trillions of gallons on a mountain, that has to go down.”

The fact that these storms hit the mountains made everything worse, and not just because of runoff. The interaction between the mountains and the storm systems wrings more moisture out of the air, Clark, Maue and Corbosiero said.

North Carolina weather officials said their top measurement total was 31.33 inches in the tiny town of Busick. Mount Mitchell also got more than 2 feet of rainfall.

Before 2017’s Hurricane Harvey, “I said to our colleagues, you know, I never thought in my career that we would measure rainfall in feet,” Clark said. “And after Harvey, Florence, the more isolated events in eastern Kentucky, portions of South Dakota. We’re seeing events year in and year out where we are measuring rainfall in feet.”

Storms are getting wetter as the climate change s, said Corbosiero and Dello. A basic law of physics says the air holds nearly 4% more moisture for every degree Fahrenheit warmer (7% for every degree Celsius) and the world has warmed more than 2 degrees (1.2 degrees Celsius) since pre-industrial times.

Corbosiero said meteorologists are vigorously debating how much of Helene is due to worsening climate change and how much is random.

For Dello, the “fingerprints of climate change” were clear.

“We’ve seen tropical storm impacts in western North Carolina. But these storms are wetter and these storms are warmer. And there would have been a time when a tropical storm would have been heading toward North Carolina and would have caused some rain and some damage, but not apocalyptic destruction. ”

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Follow AP’s climate coverage at https://apnews.com/hub/climate

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Follow Seth Borenstein on Twitter at @borenbears

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Associated Press climate and environmental coverage receives support from several private foundations. See more about AP’s climate initiative here. The AP is solely responsible for all content.

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‘Big Sam’: Paleontologists unearth giant skull of Pachyrhinosaurus in Alberta

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It’s a dinosaur that roamed Alberta’s badlands more than 70 million years ago, sporting a big, bumpy, bony head the size of a baby elephant.

On Wednesday, paleontologists near Grande Prairie pulled its 272-kilogram skull from the ground.

They call it “Big Sam.”

The adult Pachyrhinosaurus is the second plant-eating dinosaur to be unearthed from a dense bonebed belonging to a herd that died together on the edge of a valley that now sits 450 kilometres northwest of Edmonton.

It didn’t die alone.

“We have hundreds of juvenile bones in the bonebed, so we know that there are many babies and some adults among all of the big adults,” Emily Bamforth, a paleontologist with the nearby Philip J. Currie Dinosaur Museum, said in an interview on the way to the dig site.

She described the horned Pachyrhinosaurus as “the smaller, older cousin of the triceratops.”

“This species of dinosaur is endemic to the Grand Prairie area, so it’s found here and nowhere else in the world. They are … kind of about the size of an Indian elephant and a rhino,” she added.

The head alone, she said, is about the size of a baby elephant.

The discovery was a long time coming.

The bonebed was first discovered by a high school teacher out for a walk about 50 years ago. It took the teacher a decade to get anyone from southern Alberta to come to take a look.

“At the time, sort of in the ’70s and ’80s, paleontology in northern Alberta was virtually unknown,” said Bamforth.

When paleontogists eventually got to the site, Bamforth said, they learned “it’s actually one of the densest dinosaur bonebeds in North America.”

“It contains about 100 to 300 bones per square metre,” she said.

Paleontologists have been at the site sporadically ever since, combing through bones belonging to turtles, dinosaurs and lizards. Sixteen years ago, they discovered a large skull of an approximately 30-year-old Pachyrhinosaurus, which is now at the museum.

About a year ago, they found the second adult: Big Sam.

Bamforth said both dinosaurs are believed to have been the elders in the herd.

“Their distinguishing feature is that, instead of having a horn on their nose like a triceratops, they had this big, bony bump called a boss. And they have big, bony bumps over their eyes as well,” she said.

“It makes them look a little strange. It’s the one dinosaur that if you find it, it’s the only possible thing it can be.”

The genders of the two adults are unknown.

Bamforth said the extraction was difficult because Big Sam was intertwined in a cluster of about 300 other bones.

The skull was found upside down, “as if the animal was lying on its back,” but was well preserved, she said.

She said the excavation process involved putting plaster on the skull and wooden planks around if for stability. From there, it was lifted out — very carefully — with a crane, and was to be shipped on a trolley to the museum for study.

“I have extracted skulls in the past. This is probably the biggest one I’ve ever done though,” said Bamforth.

“It’s pretty exciting.”

This report by The Canadian Press was first published Sept. 25, 2024.

The Canadian Press. All rights reserved.

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The ancient jar smashed by a 4-year-old is back on display at an Israeli museum after repair

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TEL AVIV, Israel (AP) — A rare Bronze-Era jar accidentally smashed by a 4-year-old visiting a museum was back on display Wednesday after restoration experts were able to carefully piece the artifact back together.

Last month, a family from northern Israel was visiting the museum when their youngest son tipped over the jar, which smashed into pieces.

Alex Geller, the boy’s father, said his son — the youngest of three — is exceptionally curious, and that the moment he heard the crash, “please let that not be my child” was the first thought that raced through his head.

The jar has been on display at the Hecht Museum in Haifa for 35 years. It was one of the only containers of its size and from that period still complete when it was discovered.

The Bronze Age jar is one of many artifacts exhibited out in the open, part of the Hecht Museum’s vision of letting visitors explore history without glass barriers, said Inbal Rivlin, the director of the museum, which is associated with Haifa University in northern Israel.

It was likely used to hold wine or oil, and dates back to between 2200 and 1500 B.C.

Rivlin and the museum decided to turn the moment, which captured international attention, into a teaching moment, inviting the Geller family back for a special visit and hands-on activity to illustrate the restoration process.

Rivlin added that the incident provided a welcome distraction from the ongoing war in Gaza. “Well, he’s just a kid. So I think that somehow it touches the heart of the people in Israel and around the world,“ said Rivlin.

Roee Shafir, a restoration expert at the museum, said the repairs would be fairly simple, as the pieces were from a single, complete jar. Archaeologists often face the more daunting task of sifting through piles of shards from multiple objects and trying to piece them together.

Experts used 3D technology, hi-resolution videos, and special glue to painstakingly reconstruct the large jar.

Less than two weeks after it broke, the jar went back on display at the museum. The gluing process left small hairline cracks, and a few pieces are missing, but the jar’s impressive size remains.

The only noticeable difference in the exhibit was a new sign reading “please don’t touch.”

The Canadian Press. All rights reserved.

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