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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 laws of physics 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 special theory of relativity. 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 particles 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 quantum mechanics 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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Science

Scientists Tested Einstein’s Relativity on a Cosmic Scale, And Found Something Odd : ScienceAlert

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Everything in the Universe has gravity – and feels it too. Yet this most common of all fundamental forces is also the one that presents the biggest challenges to physicists.

Albert Einstein’s theory of general relativity has been remarkably successful in describing the gravity of stars and planets, but it doesn’t seem to apply perfectly on all scales.

General relativity has passed many years of observational tests, from Eddington’s measurement of the deflection of starlight by the Sun in 1919 to the recent detection of gravitational waves.

However, gaps in our understanding start to appear when we try to apply it to extremely small distances, where the laws of quantum mechanics operate, or when we try to describe the entire universe.

Our new study, published in Nature Astronomy, has now tested Einstein’s theory on the largest of scales.

We believe our approach may one day help resolve some of the biggest mysteries in cosmology, and the results hint that the theory of general relativity may need to be tweaked on this scale.

Faulty model?

Quantum theory predicts that empty space, the vacuum, is packed with energy. We do not notice its presence because our devices can only measure changes in energy rather than its total amount.

However, according to Einstein, the vacuum energy has a repulsive gravity – it pushes the empty space apart. Interestingly, in 1998, it was discovered that the expansion of the Universe is in fact accelerating (a finding awarded with the 2011 Nobel Prize in physics).

However, the amount of vacuum energy, or dark energy as it has been called, necessary to explain the acceleration is many orders of magnitude smaller than what quantum theory predicts.

Hence the big question, dubbed “the old cosmological constant problem”, is whether the vacuum energy actually gravitates – exerting a gravitational force and changing the expansion of the universe.

If yes, then why is its gravity so much weaker than predicted? If the vacuum does not gravitate at all, what is causing the cosmic acceleration?

We don’t know what dark energy is, but we need to assume it exists in order to explain the Universe’s expansion.

Similarly, we also need to assume there is a type of invisible matter presence, dubbed dark matter, to explain how galaxies and clusters evolved to be the way we observe them today.

These assumptions are baked into scientists’ standard cosmological theory, called the lambda cold dark matter (LCDM) model – suggesting there is 70 percent dark energy, 25 percent dark matter, and 5 percent ordinary matter in the cosmos. And this model has been remarkably successful in fitting all the data collected by cosmologists over the past 20 years.

But the fact that most of the Universe is made up of dark forces and substances, taking odd values that don’t make sense, has prompted many physicists to wonder if Einstein’s theory of gravity needs modification to describe the entire universe.

A new twist appeared a few years ago when it became apparent that different ways of measuring the rate of cosmic expansion, dubbed the Hubble constant, give different answers – a problem known as the Hubble tension.

The disagreement, or tension, is between two values of the Hubble constant.

One is the number predicted by the LCDM cosmological model, which has been developed to match the light left over from the Big Bang (the cosmic microwave background radiation).

The other is the expansion rate measured by observing exploding stars known as supernovas in distant galaxies.

Many theoretical ideas have been proposed for ways of modifying LCDM to explain the Hubble tension. Among them are alternative gravity theories.

Digging for answers

We can design tests to check if the universe obeys the rules of Einstein’s theory.

General relativity describes gravity as the curving or warping of space and time, bending the pathways along which light and matter travel. Importantly, it predicts that the trajectories of light rays and matter should be bent by gravity in the same way.

Together with a team of cosmologists, we put the basic laws of general relativity to test. We also explored whether modifying Einstein’s theory could help resolve some of the open problems of cosmology, such as the Hubble tension.

To find out whether general relativity is correct on large scales, we set out, for the first time, to simultaneously investigate three aspects of it. These were the expansion of the Universe, the effects of gravity on light, and the effects of gravity on matter.

Using a statistical method known as the Bayesian inference, we reconstructed the gravity of the Universe through cosmic history in a computer model based on these three parameters.

We could estimate the parameters using the cosmic microwave background data from the Planck satellite, supernova catalogs as well as observations of the shapes and distribution of distant galaxies by the SDSS and DES telescopes.

We then compared our reconstruction to the prediction of the LCDM model (essentially Einstein’s model).

We found interesting hints of a possible mismatch with Einstein’s prediction, albeit with rather low statistical significance.

This means that there is nevertheless a possibility that gravity works differently on large scales, and that the theory of general relativity may need to be tweaked.

Our study also found that it is very difficult to solve the Hubble tension problem by only changing the theory of gravity.

The full solution would probably require a new ingredient in the cosmological model, present before the time when protons and electrons first combined to form hydrogen just after the Big Bang, such as a special form of dark matter, an early type of dark energy, or primordial magnetic fields.

Or, perhaps, there’s a yet unknown systematic error in the data.

That said, our study has demonstrated that it is possible to test the validity of general relativity over cosmological distances using observational data. While we haven’t yet solved the Hubble problem, we will have a lot more data from new probes in a few years.

This means that we will be able to use these statistical methods to continue tweaking general relativity, exploring the limits of modifications, to pave the way to resolving some of the open challenges in cosmology.

Kazuya Koyama, Professor of Cosmology, University of Portsmouth and Levon Pogosian, Professor of Physics, Simon Fraser University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Science

Einstein’s Mind-Bending Theory of Relativity Passes Yet Another Huge Test

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What’s happening

Scientists sent a satellite to space to test Einstein’s weak-equivalence principle with extreme precision.

Why it matters

The weak-equivalence principle is integral to general relativity, so these test results offer yet more support for a core theory of our universe.

In 1916, Albert Einstein dared to declare that Isaac Newton was wrong about gravity. No, he said, it’s not a mysterious force emanating from Earth. 

Instead, Einstein imagined that space and time are twisted in an interdimensional grid, and the laces of this grid are like unwound paper clips. Bendable; moldable. It’s only because we exist inside this sort of intangible mesh, he believed, that our simple human bodies experience the facade of a force holding us to the ground. We call that gravity. 

(If that hurt your brain, don’t worry, here’s an article dedicated to breaking down this concept.)

And while the genius mathematician referred to this perplexing notion as his theory of general relativity, a title that stuck, his peers called it “totally impractical and absurd,” a title that didn’t. Against all odds, Einstein’s mind-numbing idea has yet to falter. Its premises remain true on both the smallest of scales and the incomprehensibly large. Experts have attempted to poke holes in them again, and again and again, but general relativity always prevails. 

And on Wednesday, thanks to an ambitious satellite experiment, scientists announced that, yet again, general relativity has proven itself to be a fundamental truth of our universe. The team conducted what it calls the “most precise test” of one of general relativity’s key aspects, named the weak-equivalence principle, with a mission dubbed Microscope. 

“I have been working on this subject for more than 20 years, and I realize the luck I had to be the project manager of the science instrument and the co-investigator of this mission,” said Manuel Rodrigues, a scientist at French aerospace lab ONERA and author of a new study, published in the journal Physical Review Letters. 

“This is very rare to leave such a remarkable result in physics history.”

https://www.cnet.com/a/img/resize/7731330030bfb14f98564dd36af86d14628614a7/hub/2022/06/13/320a9d1e-3ea1-4303-9bfb-73e00f0782fa/img2.gif?auto=webp&format=mp4&width=1200

A depiction of how Einstein’s relativity imagines the universe.


Zooey Liao/CNET

What’s the weak-equivalence principle?

The weak-equivalence principle is a weird one.

It pretty much says all objects in a gravitational field must fall in the same way when no other force is acting on them — I’m talking external interference like wind, a person kicking the object, another object bumping into it, you get the idea. 

And yes, when I say all objects, I mean all objects. A feather; a piano; a basketball; you and me; anything you can imagine, really, according to this principle must fall in the exact same way.

The Microscope project sent a satellite into Earth’s orbit that contained two objects: a platinum alloy and titanium alloy. “The selection was based on technology considerations,” Rodrigues said, such as whether the materials were easy and feasible to make in a lab. 

But most importantly for understanding the weak-equivalence principle, or WEP, these alloys were blasted into Earth’s orbit because stuff up there exists in our planet’s gravitational field without any other forces acting on them. Perfect for the testing criteria. Once the satellite was in space, the researchers began testing, for years, whether the platinum bit and titanium bit fell in the same way as they orbited Earth.

They did — to an extremely precise degree. 

“The most thrilling part during the project was to develop an instrument and a mission that nobody has done before at such a level of accuracy — a new world to explore,” Rodrigues said. “As the pioneers of this new world, we expected at each moment to face phenomena that were not seen before because we were the first to enter.”

A capsule used during the Microscope mission.


ZARM/Selig – ONERA 2013

If you’re into the technicalities, the results of the experiment showed that the acceleration of one alloy’s fall differed from the other by no more than one part in 10^15. A difference beyond this quantity, the researchers say, would mean the WEP is violated by our current understanding of Einstein’s theory. 

For the future, the team is working on a follow-up mission called Microscope 2, which Rodrigues says will test the weak-equivalence principle 100 times better.

However, this is probably as good as it’s going to get for at least a decade or so, the researchers say. 

Great, what does this mean for me?

In a way, general relativity theory’s solidity is kind of a problem. That’s because even though it’s an essential blueprint for understanding our universe, it isn’t the only blueprint.

We also have constructs like the standard model of particle physics, which explains how things such as atoms and bosons work, and quantum mechanics, which accounts for things like electromagnetism and the uncertainty of existence.

But here’s the caveat.

Both of these concepts seem just as unbreakable as general relativity, yet aren’t compatible with it. So… something must be wrong. And that something is preventing us from creating a unified story of the physical universe. The standard model, for instance, famously can’t explain gravity, and general relativity doesn’t really consider quantum phenomena. It’s like a huge battle to be the ultimate theory.

The Microscope team standing with the satellite equipment, to the right.


ONERA/Rodrigues 2016

“Some theories expect a coupling between gravitation and some electromagnetic parameters,” Rodrigues offered as an example. “This coupling doesn’t exist in Einstein’s theory, that is why the WEP exists.” 

We find ourselves at a crossroads.

But the bright side is that the vast majority of scientists consider all of these theories to be unfinished. Thus, if we can somehow find a way to finish them – locate a new coupling, for instance, as Rodrigues says, or identify a new particle to add to the standard model – that might lead us to the missing pieces of our universe’s puzzle. 

“It should be a revolution in physics,” Rodrigues said, of breaking the WEP. “It will mean that we find a new force, or maybe a new particle like the graviton – it is the grail of the physicist.”

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Science

A Core Principle of General Relativity Just Passed Its Strictest Test Yet : ScienceAlert

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A core principle of Einstein’s general theory of relativity has just passed its most stringent test yet.

Using a specially designed satellite, an international team of scientists measured the accelerations of pairs of free-falling objects in Earth’s orbit. Results based on five months’ worth of data indicated the accelerations didn’t differ by more than one part in 1015, ruling out any violations to the weak equivalence principle down to that scale.

The weak equivalence principle is relatively simple to observe, stating all objects accelerate identically in the same gravitational field when no other influences act upon them, regardless of their mass or composition.

It was perhaps most famously demonstrated to dramatic effect in 1971 when astronaut Dave Scott dropped a hammer and a feather simultaneously from the same height while standing on the Moon. Without air resistance to slow the feather, the two objects dropped to the Moon’s surface at the same speed.

The new experiment, called MICROSCOPE and headed by the late physicist Pierre Touboul, was somewhat more rigorous than Scott’s demonstration. It involved a satellite circling over Earth in orbit from April 25, 2016 until deactivation on October 18, 2018.

During this time, the team ran multiple experiments using masses suspended in free-fall, providing a total of five months of data. Two-thirds of this data involved pairs of test masses of different compositions, alloys of titanium and platinum. The remaining third involved a reference pair of masses of the same platinum composition.

The experimental equipment used electrostatic forces to keep the two test masses in the same position relative to one another. If there was any difference in the acceleration – a metric known as the Eötvös ratio – the equipment would register changes in the electrostatic forces holding the masses in place.

Early results released in 2017 were promising, finding no violation of the weak equivalence principle down to an Eötvös parameter of −1±9 x 10−15. However, the satellite was still operational, and producing data, which meant the work was not complete. The full dataset cements those early findings, constraining the Eötvös parameter to 1.1 x 10−15.

This is the tightest bound on the weak equivalence principle to date, and unlikely to be exceeded soon. It means that scientists can continue to rely on general relativity with more confidence than ever, and place new constraints on the intersection between general relativity and quantum mechanics, two regimes that operate under different rules.

“We have new and much better constraints for any future theory, because these theories must not violate the equivalence principle at this level,” explains astronomer Gilles Métris of Côte d’Azur Observatory in France.

This is a spectacular result, given that the equipment, designed to work in the microgravity environment of Earth orbit, could not be tested before launching. Now that the MICROSCOPE project has been successfully completed, the team can use the results to design an even more stringent test.

These tests will help probe the limitations of general relativity, a framework that describes gravitation in physical space-time. On atomic and subatomic scales, however, general relativity breaks down, and quantum mechanics takes over. Scientists have been trying to resolve the differences between the two for quite some time. Figuring out precisely where general relativity breaks down could be one way to do it.

We know now that that breakdown does not occur down to one part in 1015 for weak equivalence. Specific improvements that can be made to the next iteration of the satellite could probe it down to the level of one part in 1017. That is going to take some time to accomplish, however.

“For at least one decade or maybe two, we don’t see any improvement with a space satellite experiment,” says physics engineer Manuel Rodrigues of the French national aerospace research centre (ONERA).

But we suspect these results will be quite enough to be getting on with for the time being.

The team’s incredible work has been published in Physical Review Letters and a special issue of Classical and Quantum Gravity.

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Putting the Theory of Special Relativity Into Practice

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The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity published in 1905 and general relativity published in 1915. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature.

The theory of relativity was developed by Albert Einstein in the early 1900s due to the inability of classical physics to explain certain observations. It has two components, special relativity and general relativity.

Special relativity is based on the key concepts of a constant speed of light and physical events must look the same to all observers and applies to all physical phenomena without significant gravitation. General relativity is the idea that space and time are two aspects of spacetime, and what we perceive as gravity is the warping of spacetime.

Scientists who study the cosmos have a favorite philosophy known as the “mediocrity principle,” which, in essence, suggests that there’s really nothing special about Earth, the Sun, or the

This image made from a composite of September 2003 – January 2004 photos captured by the NASA/ESA Hubble Space Telescope shows nearly 10,000 galaxies in the deepest visible-light image of the cosmos, cutting across billions of light-years. Credit: Image courtesy of NASA, ESA, S. Beckwith (STScI), HUDF Team

“What this research is telling us is that we have a funny motion, but that funny motion is consistent with everything we know about the universe—there’s nothing special going on here,” said Darling. “We’re not special as a galaxy or as observers.”

Roughly 35 years ago, researchers discovered the cosmic microwave background, which is electromagnetic radiation left over from the universe’s formation during the

Astrophysics professor Jeremy Darling studies galaxy evolution, massive black holes, star formation, and cosmology. Credit: University of Colorado at Boulder

Scientists can independently test this inference by counting the galaxies that are visible from Earth or adding up their brightness. They can do this thanks largely to Albert Einstein’s 1905 theory of special relativity, which explains how speed affects time and space. In this application, a person on Earth looking out into the universe in one direction—the same direction that the Sun and the Earth are moving—should see galaxies that are brighter, bluer, and more concentrated. Similarly, by looking in the other direction, the person should see galaxies that are darker, redder, and spaced farther apart.

But when investigators have tried to count galaxies in recent years—a process that’s difficult to do accurately—they’ve come up with numbers that suggest the Sun is moving much faster than previously thought, which is at odds with standard cosmology.

“It’s hard to count galaxies over the whole sky—you’re usually stuck with a hemisphere or less,” said Darling. “And, on top of that, our own galaxy gets in the way. It has dust that will cause you to find fewer galaxies and will make them look dimmer as you get closer to our galaxy.”

Darling was intrigued and perplexed by this cosmological puzzle, so he decided to investigate for himself. He also knew there were two recently released surveys that could help improve the

“I love the idea that this basic principle that Einstein told us about a long time ago is something you can see. It’s a really esoteric thing that seems super weird, but if you go out and count galaxies, you could see this neat effect. It’s not quite as esoteric or weird as you might think.” — Jeremy Darling

Together, these surveys allowed Darling to study the entire sky by patching together views from the northern and southern hemispheres. Importantly, the new surveys also used radio waves, which made it easier to “see” through the dust of the Milky Way, thus improving the view of the universe.

When Darling analyzed the surveys, he found that the number of galaxies and their brightness was in perfect agreement with the velocity researchers had previously inferred from the cosmic microwave background.

“We find a bright direction and a dim direction—we find a direction where there are more galaxies and a direction where there are fewer galaxies,” he said. “The big difference is that it lines up with the early universe from the cosmic microwave background and it has the right speed. Our cosmology is just fine.”

Because Darling’s findings differ from past results, his paper will likely prompt various follow-up studies to confirm or dispute his results.

But in addition to pushing the field of cosmology forward, the findings are a good real-world example of Einstein’s special relativity theory—and they demonstrate how researchers are still putting the theory into practice, more than 100 years after the famed physicist first proposed it.

“I love the idea that this basic principle that Einstein told us about a long time ago is something you can see,” Darling said. “It’s a really esoteric thing that seems super weird, but if you go out and count galaxies, you could see this neat effect. It’s not quite as esoteric or weird as you might think.”

Reference: “The Universe is Brighter in the Direction of Our Motion: Galaxy Counts and Fluxes are Consistent with the CMB Dipole” by Jeremy Darling, 26 May 2022, Astrophysical Journal Letters.
DOI: 10.3847/2041-8213/ac6f08