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Warp drives: Physicists give chances of faster-than -light space travel a boost

Associate Professor of Physics, Oklahoma State University

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Mario Borunda does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Oklahoma State University provides funding as a member of The Conversation US.

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The closest star to Earth is Proxima Centauri. It is about 4.25 light-years away, or about 25 trillion miles (40 trillion km). The fastest ever spacecraft, the now- in-space Parker Solar Probe will reach a top speed of 450,000 mph. It would take just 20 seconds to go from Los Angeles to New York City at that speed, but it would take the solar probe about 6,633 years to reach Earth’s nearest neighboring solar system.

If humanity ever wants to travel easily between stars, people will need to go faster than light. But so far, faster-than-light travel is possible only in science fiction.

In Issac Asimov’s Foundation series , humanity can travel from planet to planet, star to star or across the universe using jump drives. As a kid, I read as many of those stories as I could get my hands on. I am now a theoretical physicist and study nanotechnology, but I am still fascinated by the ways humanity could one day travel in space.

Some characters – like the astronauts in the movies “Interstellar” and “Thor” – use wormholes to travel between solar systems in seconds. Another approach – familiar to “Star Trek” fans – is warp drive technology. Warp drives are theoretically possible if still far-fetched technology. Two recent papers made headlines in March when researchers claimed to have overcome one of the many challenges that stand between the theory of warp drives and reality.

But how do these theoretical warp drives really work? And will humans be making the jump to warp speed anytime soon?

Compression and expansion

Physicists’ current understanding of spacetime comes from Albert Einstein’s theory of General Relativity . General Relativity states that space and time are fused and that nothing can travel faster than the speed of light. General relativity also describes how mass and energy warp spacetime – hefty objects like stars and black holes curve spacetime around them. This curvature is what you feel as gravity and why many spacefaring heroes worry about “getting stuck in” or “falling into” a gravity well. Early science fiction writers John Campbell and Asimov saw this warping as a way to skirt the speed limit.

What if a starship could compress space in front of it while expanding spacetime behind it? “Star Trek” took this idea and named it the warp drive.

In 1994, Miguel Alcubierre, a Mexican theoretical physicist, showed that compressing spacetime in front of the spaceship while expanding it behind was mathematically possible within the laws of General Relativity . So, what does that mean? Imagine the distance between two points is 10 meters (33 feet). If you are standing at point A and can travel one meter per second, it would take 10 seconds to get to point B. However, let’s say you could somehow compress the space between you and point B so that the interval is now just one meter. Then, moving through spacetime at your maximum speed of one meter per second, you would be able to reach point B in about one second. In theory, this approach does not contradict the laws of relativity since you are not moving faster than light in the space around you. Alcubierre showed that the warp drive from “Star Trek” was in fact theoretically possible.

Proxima Centauri here we come, right? Unfortunately, Alcubierre’s method of compressing spacetime had one problem: it requires negative energy or negative mass.

A negative energy problem

Alcubierre’s warp drive would work by creating a bubble of flat spacetime around the spaceship and curving spacetime around that bubble to reduce distances. The warp drive would require either negative mass – a theorized type of matter – or a ring of negative energy density to work. Physicists have never observed negative mass, so that leaves negative energy as the only option.

To create negative energy, a warp drive would use a huge amount of mass to create an imbalance between particles and antiparticles. For example, if an electron and an antielectron appear near the warp drive, one of the particles would get trapped by the mass and this results in an imbalance. This imbalance results in negative energy density. Alcubierre’s warp drive would use this negative energy to create the spacetime bubble.

But for a warp drive to generate enough negative energy, you would need a lot of matter. Alcubierre estimated that a warp drive with a 100-meter bubble would require the mass of the entire visible universe .

In 1999, physicist Chris Van Den Broeck showed that expanding the volume inside the bubble but keeping the surface area constant would reduce the energy requirements significantly , to just about the mass of the sun. A significant improvement, but still far beyond all practical possibilities.

A sci-fi future?

Two recent papers – one by Alexey Bobrick and Gianni Martire and another by Erik Lentz – provide solutions that seem to bring warp drives closer to reality.

Bobrick and Martire realized that by modifying spacetime within the bubble in a certain way, they could remove the need to use negative energy. This solution, though, does not produce a warp drive that can go faster than light.

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Independently, Lentz also proposed a solution that does not require negative energy. He used a different geometric approach to solve the equations of General Relativity, and by doing so, he found that a warp drive wouldn’t need to use negative energy. Lentz’s solution would allow the bubble to travel faster than the speed of light.

It is essential to point out that these exciting developments are mathematical models. As a physicist, I won’t fully trust models until we have experimental proof. Yet, the science of warp drives is coming into view. As a science fiction fan, I welcome all this innovative thinking. In the words of Captain Picard , things are only impossible until they are not.

• General Relativity
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This Trick Flips Space and Time

By Meddling With Spacetime Dimensions, We Could Finally Reach Warp Speed

New research shows that the “superluminal observer” needs three separate time dimensions for a warp-speed math trick that would please even Galileo.

✅ Quick Facts:

• In new research, the lead scientist explains why just one space and one time aren’t enough for this scenario.
• Symmetry is a physics concept that goes all the way back to Galileo’s time.

The secret to faster-than-light physics could be to double down on the number of dimensions. Specifically, the solution may lie in three dimensions of time , with just one representing space. The math is deep and complicated, but the ideas may be within our grasp after all. And there’s one math trick at superspeeds that may just “flip” your lid.

The key idea at play is that of a “superluminal observer,” according to research published in December 2022 in the journal Classical and Quantum Gravity. “Superluminal” means faster than light, from super - meaning “more” or “most,” and - luminal like, well, Lumière from Beauty and the Beast, and the lumens that power your home movie projector. The superluminal observer is a hypothetical thing that is looking at the universe while traveling faster than light. It’s you in your Star Trek warp-speed shuttle.

Superluminal observers are cool because, in a way, they marry together two very different sides of physics: general relativity and quantum mechanics . General relativity is the work embodied by Albert Einstein, which governs how spacetime functions as bodies move around the universe at subluminal, or slower than light, speeds. Quantum mechanics explains how subatomic particles behave, or don’t behave, in very strange ways on the smallest of scales.

The research team—led by theoretical physicist Andrzej Dragan of the University of Warsaw and the National University of Singapore—has theorized that many parts of quantum physics, like indeterminism and superposition , can be explained if you take general relativity and apply its principles to the superluminal observer. In other words, how messy does spacetime get if we take our shuttle up to warp speed? Is everything suddenly in multiple places at once?

Dragan’s new work indicates that it’s at least a possibility. Perhaps more interestingly, the way general relativity becomes quantum phenomena at speeds greater than light doesn’t seem to introduce any causal paradoxes. In earlier work , published in the New Journal of Physics in March 2020, Dragan and his coauthor studied “just” one space dimension and one time dimension, known as 1+1. In the new paper, the researchers upped the ante to include one space dimension and three time dimensions, or 1+3.

When Time and Space Flip Math

Why do we need three time dimensions? To understand, we have to talk about some math. “[D]espite our common perception, time and space are strikingly similar according to relativity, and mathematically the only difference between them is the minus sign somewhere in the equations,” Dragan explains to Popular Mechanics in an email. That’s a small difference in complicated math, but think of the algebra example of the difference of two squares: x² - 16, for example, is the result of (x - 4)(x + 4). With one flipped sign, the middle term in the polynomial falls away.

But when the observer is going faster than the speed of light, the difference in signs also changes. That’s because time and space must flip in the math. “The time of the superluminal observer becomes space of the subluminal one, and their space becomes time,” Dragan says. In other words, the regular, non-light-speed observer’s space and time turn into the time and space, relatively, of the faster-than-light observer. “So their corresponding signs have to interchange.”

In a 1+1 scenario, that means the two dimensions are the same, making it redundant. If 50 = 50, does it matter which 50 is which? (In logic, we call this a tautology.) That means that if we want to truly study space and time as different things, we have to add a second “set” of two dimensions: space and time 1, together, represent space; while time 2 and time 3, together, represent time . It’s not quite the difference of two squares, but we have two balanced sets of dimensions.

The Symmetry in Physics

There’s another interesting aspect to this research, because Dragan’s team wants to show that even at superluminal speeds, physics shows symmetry.

“The idea of symmetry in physics can be traced back to Galileo,” Dragan says. “He noticed that no matter what velocity we move at, as long as that velocity is constant, our physics remains the same. A parrot flying in a moving ship experiences the same dynamical laws as at ‘rest’ on Earth.”

✅ Galileo Galilei was an influential Italian scientist who lived during the 16th and 17th centuries. As an elderly man, he received a life sentence for going public with his belief that Earth orbited the sun!

But our conceptions of physics are limited by the long-running (and reasonable!) belief that nothing can travel faster than light, Dragan explains. That means the superluminal observer, by definition, exists as a kind of exception into which we must work to extend the idea of symmetry. Does it make sense that a superluminal observer would still be subject to symmetry? Is the parrot traveling faster than light still the same as the parrot in the ship or on Earth?

“We argued that this additional limiting assumption isn’t necessary,” Dragan says. He believes symmetry may extend into faster-than-light speeds, and our parrot friend would be just as affected by the same laws of physics while traveling in the warp-speed shuttle.

Toward a Grand Unified Theory

So, this paper isn’t about traveling at warp speed, but instead an analysis of physics to show how we can bring two very different physics branches together. Why is that, itself, so important?

“The idea of more than one time dimension has been considered by others over the years, so that particular premise is not novel,” Harold “Sonny” White, a onetime NASA physicist and the founder of the Limitless Space Institute (LSI), a group that funds and promotes far-out space travel and physics research, tells Popular Mechanics . “But the mathematical framework developed by the authors in this published paper is unique. It would seem the authors’ perceived benefit from the effort is that it establishes a mathematical basis for why we need a field theoretical framework.”

What is a field theoretical framework? It’s the big picture of physics that can bring everything together. “[I]f we envision the standard models of physics as a Venn diagram, there would be two circles side-by-side that touch at a single tangent point,” White explains. “The idea of a grand unified field theory might be envisioned as a larger circle that encircles both the smaller circles.”

By showing their work, these researchers have pointed out a really specific way in which one big basket of physics—rather than two baskets that we aren’t sure how to carry at the same time—would make more sense in practical and mathematical terms.

Okay, sure, you may be thinking: all this superluminal jabberwocky is interesting. But warp speed itself is science fiction, right? (At least for now: White’s LSI funds education that may eventually lead us elsewhere.) The superluminal observer is just a thought exercise ... right?

Dragan isn’t so sure. “The last remaining question is whether superluminal objects are only a mathematical possibility, or they actually exist in reality,” he concludes. “We believe the latter to be that case, and that is the purpose of our further research.”

That means our warp-speed shuttle, once the most far-out thing science fiction writers could even imagine, could embody an elegant theory that brings together two very different kinds of physics. Indeed, objects in the superluminal mirror may be closer than they appear.

Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all. 

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Can anything travel faster than the speed of light?

Does it matter if it's in a vacuum?

In 1676, by studying the motion of Jupiter's moon Io, Danish astronomer Ole Rømer calculated that light travels at a finite speed. Two years later, building on data gathered by Rømer, Dutch mathematician and scientist Christiaan Huygens became the first person to attempt to determine the actual speed of light, according to the American Museum of Natural History in New York City. Huygens came up with a figure of 131,000 miles per second (211,000 kilometers per second), a number that isn't accurate by today's standards — we now know that the speed of light in the "vacuum" of empty space is about 186,282 miles per second (299,792 km per second) — but his assessment showcased that light travels at an incredible speed.

According to Albert Einstein 's theory of special relativity , light travels so fast that, in a vacuum, nothing in the universe is capable of moving faster. 

"We cannot move through the vacuum of space faster than the speed of light," confirmed Jason Cassibry, an associate professor of aerospace engineering at the Propulsion Research Center, University of Alabama in Huntsville.

Question answered, right? Maybe not. When light is not in a vacuum, does the rule still apply?

Related: How many atoms are in the observable universe?

"Technically, the statement 'nothing can travel faster than the speed of light' isn't quite correct by itself," at least in a non-vacuum setting, Claudia de Rham, a theoretical physicist at Imperial College London, told Live Science in an email. But there are certain caveats to consider, she said. Light exhibits both particle-like and wave-like characteristics, and can therefore be regarded as both a particle (a photon ) and a wave. This is known as wave-particle duality.

If we look at light as a wave, then there are "multiple reasons" why certain waves can travel faster than white (or colorless) light in a medium, de Rham said. One such reason, she said, is that "as light travels through a medium — for instance, glass or water droplets — the different frequencies or colors of light travel at different speeds." The most obvious visual example of this occurs in rainbows, which typically have the long, faster red wavelengths at the top and the short, slower violet wavelengths at the bottom, according to a post by the University of Wisconsin-Madison . 

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When light travels through a vacuum, however, the same is not true. "All light is a type of electromagnetic wave, and they all have the same speed in a vacuum (3 x 10^8 meters per second). This means both radio waves and gamma rays have the same speed," Rhett Allain, a physics professor at Southeastern Louisiana University, told Live Science in an email.

So, according to de Rham, the only thing capable of traveling faster than the speed of light is, somewhat paradoxically, light itself, though only when not in the vacuum of space. Of note, regardless of the medium, light will never exceed its maximum speed of 186,282 miles per second.

Universal look

According to Cassibry, however, there is something else to consider when discussing things moving faster than the speed of light.

"There are parts of the universe that are expanding away from us faster than the speed of light, because space-time is expanding," he said. For example, the Hubble Space Telescope recently spotted 12.9 billion year-old light from a distant star known as Earendel. But, because the universe is expanding at every point, Earendel is moving away from Earth and has been since its formation, so the galaxy is now 28 billion light years away from Earth.

In this case, space-time is expanding, but the material in space-time is still traveling within the bounds of light speed.

Related: Why is space a vacuum?

So, it's clear that nothing travels faster than light that we know of, but is there any situation where it might be possible? Einstein's theory of special relativity, and his subsequent theory of general relativity, is "built under the principle that the notions of space and time are relative," de Rham said. But what does this mean? "If someone [were] able to travel faster than light and carry information with them, their notion of time would be twisted as compared to ours," de Rham said. "There could be situations where the future could affect our past, and then the whole structure of reality would stop making sense."

This would indicate that it would probably not be desirable to make a human travel faster than the speed of light. But could it ever be possible? Will there ever be a time when we are capable of creating craft that could propel materials — and ultimately humans — through space at a pace that outstrips light speed? "Theorists have proposed various types of warp bubbles that could enable faster-than-light travel," Cassibry said.

But is de Rham convinced?

"We can imagine being able to communicate at the speed of light with systems outside our solar system ," de Rham said. "But sending actual physical humans at the speed of light is simply impossible, because we cannot accelerate ourselves to such speed.

"Even in a very idealistic situation where we imagine we could keep accelerating ourselves at a constant rate — ignoring how we could even reach a technology that could keep accelerating us continuously — we would never actually reach the speed of light," she added. "We could get close, but never quite reach it."

Related: How long is a galactic year?

This is a point confirmed by Cassibry. "Neglecting relativity, if you were to accelerate with a rate of 1G [Earth gravity], it would take you a year to reach the speed of light. However, you would never really reach that velocity because as you start to approach lightspeed, your mass energy increases, approaching infinite. "One of the few known possible 'cheat codes' for this limitation is to expand and contract spacetime, thereby pulling your destination closer to you. There seems to be no fundamental limit on the rate at which spacetime can expand or contract, meaning we might be able to get around this velocity limit someday."

— What would happen if the speed of light were much lower?

— What if the speed of sound were as fast as the speed of light?

— How does the rubber pencil illusion work?

Allain is similarly confident that going faster than light is far from likely, but, like Cassibry, noted that if humans want to explore distant planets, it may not actually be necessary to reach such speeds. "The only way we could understand going faster than light would be to use some type of wormhole in space," Allain said. "This wouldn't actually make us go faster than light, but instead give us a shortcut to some other location in space."

Cassibry, however, is unsure if wormholes will ever be a realistic option.

"Wormholes are theorized to be possible based on a special solution to Einstein's field equations," he said. "Basically, wormholes, if possible, would give you a shortcut from one destination to another. I have no idea if it's possible to construct one, or how we would even go about doing it." Originally published on Live Science.

Joe Phelan is a journalist based in London. His work has appeared in VICE, National Geographic, World Soccer and The Blizzard, and has been a guest on Times Radio. He is drawn to the weird, wonderful and under examined, as well as anything related to life in the Arctic Circle. He holds a bachelor's degree in journalism from the University of Chester. 

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March 9, 2021

Breaking the warp barrier for faster-than-light travel

by University of Göttingen

If travel to distant stars within an individual's lifetime is going to be possible, a means of faster-than-light propulsion will have to be found. To date, even recent research about superluminal (faster-than-light) transport based on Einstein's theory of general relativity would require vast amounts of hypothetical particles and states of matter that have 'exotic' physical properties such as negative energy density. This type of matter either cannot currently be found or cannot be manufactured in viable quantities. In contrast, new research carried out at the University of Göttingen gets around this problem by constructing a new class of hyper-fast 'solitons' using sources with only positive energies that can enable travel at any speed. This reignites debate about the possibility of faster-than-light travel based on conventional physics. The research is published in the journal Classical and Quantum Gravity .

The author of the paper, Dr. Erik Lentz, analyzed existing research and discovered gaps in previous 'warp drive' studies. Lentz noticed that there existed yet-to-be explored configurations of space-time curvature organized into 'solitons' that have the potential to solve the puzzle while being physically viable. A soliton—in this context also informally referred to as a 'warp bubble'—is a compact wave that maintains its shape and moves at constant velocity. Lentz derived the Einstein equations for unexplored soliton configurations (where the space-time metric's shift vector components obey a hyperbolic relation), finding that the altered space-time geometries could be formed in a way that worked even with conventional energy sources. In essence, the new method uses the very structure of space and time arranged in a soliton to provide a solution to faster-than-light travel , which—unlike other research—would only need sources with positive energy densities. No exotic negative energy densities needed.

If sufficient energy could be generated, the equations used in this research would allow space travel to Proxima Centauri, our nearest star, and back to Earth in years instead of decades or millennia. That means an individual could travel there and back within their lifetime. In comparison, the current rocket technology would take more than 50,000 years for a one-way journey. In addition, the solitons (warp bubbles) were configured to contain a region with minimal tidal forces such that the passing of time inside the soliton matches the time outside: an ideal environment for a spacecraft. This means there would not be the complications of the so-called 'twin paradox' whereby one twin traveling near the speed of light would age much more slowly than the other twin who stayed on Earth: in fact, according to the recent equations both twins would be the same age when reunited.

"This work has moved the problem of faster-than-light travel one step away from theoretical research in fundamental physics and closer to engineering. The next step is to figure out how to bring down the astronomical amount of energy needed to within the range of today's technologies, such as a large modern nuclear fission power plant. Then we can talk about building the first prototypes," says Lentz.

Currently, the amount of energy required for this new type of space propulsion drive is still immense. Lentz explains, "The energy required for this drive traveling at light speed encompassing a spacecraft of 100 meters in radius is on the order of hundreds of times of the mass of the planet Jupiter. The energy savings would need to be drastic, of approximately 30 orders of magnitude to be in range of modern nuclear fission reactors." He goes on to say: "Fortunately, several energy-saving mechanisms have been proposed in earlier research that can potentially lower the energy required by nearly 60 orders of magnitude." Lentz is currently in the early-stages of determining if these methods can be modified, or if new mechanisms are needed to bring the energy required down to what is currently possible.

Provided by University of Göttingen

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Faster-than-light travel: Is warp drive really possible?

A NASA scientist recently released a report analysing the feasibility of warp drive as a means of faster-than-light travel. Could this Star Trek technology really be possible?

In the Universe of Star Trek , humanity ventures out into the Galaxy on 5 April 2063 with the first ever journey on a ship capable of faster-than-light travel. The newly-invented ‘warp drive’ not only lets humans explore the cosmos, but attracts the attention of Vulcans and brings about our first contact with an alien species.

It’s been 54 years since we were first introduced to the Enterprise , and many of Star Trek ’s futuristic technologies have since been invented, from handheld communicators to universal translators. Warp drive is the next obvious choice: Voyager 1, which has travelled furthest from Earth of any spacecraft, took nearly 35 years to leave the Solar System. Not exactly handy for interstellar travel.

Luckily for humanity, theoretical physicists have been working on it. In May 2020, NASA scientist Harold “Sonny” White released an internal feasibility report discussing the technology from the point of view of ‘early mission planning’.

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The first scientific theory of warp drive came about in 1994, when theoretical physicist Miguel Alcubierre used Einstein’s theory of General Relativity to develop a framework that would allow faster-than-light travel within the confines of the laws of physics. The key that makes it possible is that, technically, the ship itself doesn’t travel faster than light.

“What warp drive is doing is basically saying that there is no law of physics that says space-time itself can't go faster than the speed of light,” says Dr Erin Macdonald , astrophysicist and science consultant for Star Trek .

“And so the concept of warp drive is to say, all right, let's take our ship, let's build a bubble of space-time around it, and then we'll have that propel us faster than the speed of light,” she says. It’s similar to the idea of a racecar driving onboard a train: someone standing by the tracks would see the car travelling much faster than its top speed.

According to General Relativity, the Universe is a flat sheet of space-time which is warped by any object with mass. “We think of the bowling ball on the trampoline and that bowling ball dips the trampoline down,” says Macdonald, “and that's what mass does to space-time.” This distortion of space-time is what we experience as gravity.

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The Alcubierre drive uses the same concept. The ‘bubble’ surrounding the ship is an area of space-time that is compressed in front of the ship and expanded behind it. As with gravity, you could create this distortion using a large amount of mass. Alternatively, thanks to Einstein’s E = mc 2 (energy is equal to mass, times the speed of light squared), you could equally use a huge amount of energy.

Inside the bubble, space-time is completely flat, meaning the space travellers wouldn’t notice any strange, relativistic effects. The result is that the bubble of space-time is hurled across the Universe, with the travellers sitting comfortably inside their ship, speedometer still reading the same number.

Unfortunately, actually creating a warp drive is even harder than it sounds. “You have to have a very, very large amount of energy,” says José Natário , Associate Professor in mathematics at the Instituto Superior Técnico in the University of Lisbon.

“To have the deformation that you need for this kind of thing to work, you'd need much, much more energy than the Sun or the Galaxy,” he says. “But also, it’s negative energy.”

Read more from Erin Macdonald:

• Star Trek Picard premiere: solving plot holes, supernovae and our Sun’s fate
• The science of Picard with Dr Erin Macdonald

Negative energy is not something that we can currently create – certainly not in the quantities needed to power a warp drive. How could energy be negative at all?

One way to think about it is to consider a particle with negative mass. These particles would react to gravity in the exact opposite way to particles of positive mass. Instead of being pulled towards a planet or star, they would be thrown away.

“If we had some sort of component like that where we had a negative mass, whatever is keeping that mass together would be that negative energy,” says Macdonald.

This isn’t a problem that will go away with refining the idea, either: Natário proved mathematically that any form of warp drive will require negative energy.

Joseph Agnew is a graduate student at the University of Alabama in Huntsville whose undergraduate work on warp drive was published in the AIAA journal . He thinks that more research into the fundamentals of physics is the way forward for warp drive.

"Further experimental study of naturally occurring gravitational waves and perhaps a study on trying to generate artificial gravitational waves would really advance the understanding of gravity, and therefore spacetime and all the connected science," Agnew says.

Natário believes there’s an even greater problem with the concept of the Alcubierre drive. Imagine a supersonic aircraft travelling faster than the speed of sound. You don’t hear the aircraft until it has already gone past, because the sound waves can’t keep up. The warp drive experiences the same effect with light waves, meaning there is no way to send a message ahead of you.

“I call it the 'you need one to make one' problem,” says Natário. How do you create the warped space-time geometry around your ship? First, you would need to send a signal ahead of you to ‘tell’ space-time to warp, Natário says. “To make it go faster than light, you need something that would be going faster than light to begin with so that you'd be able to communicate outside the horizon.”

These two problems – combined with the slight issue that the travelers would be bombarded with incredibly high-energy radiation – are the downfall of warp drive, Nátario believes. “The bottom line is, in my opinion, it's completely impossible,” he says.

Read more from Reality Check :

• Why are so many people playing Animal Crossing?
• Peaceful protests: Are non-violent demonstrations an effective way to achieve change?

Agnew is more optimistic. "Many of these theoretical space transportation concepts rely extensively on a thorough understanding of gravity and spacetime, which just isn't the case currently," he says.

"I don't yet see any way we can say, with absolute certainty, that it will 'never happen in a million years'. When in doubt, history dictates it's better to err on the side of cautious, scientific optimism."

Macdonald, too, is hopeful. “I'm an eternal optimist with this because I want to join Starfleet,” she says. “The way I think about it is it's like we never know what's going to come down the pipe with sort of these weird, exotic, fun thought experiments.

“I agree at this stage, right now, it's a fun thought experiment. But that's not to preclude some massive discovery that may happen that we can't predict.”

Visit the BBC's Reality Check website at bit.ly/reality_check_ or follow them on Twitter @BBCRealityCheck

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What If You Traveled Faster Than the Speed of Light?

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When we were kids, we were amazed that Superman could travel "faster than a speeding bullet." We could even picture him, chasing down a projectile fired from a weapon, his right arm outstretched, his cape rippling behind him. If he traveled at half the bullet 's speed, the rate at which the bullet moved away from him would halve. If he did indeed travel faster than the bullet, he would overtake it and lead the way. Go, Superman!

In other words, Superman's aerial antics obeyed Newton's views of space and time : that the positions and motions of objects in space should all be measurable relative to an absolute, nonmoving frame of reference [source: Rynasiewicz ].

In the early 1900s, scientists held firm to the Newtonian view of the world. Then a German-born mathematician and physicist by the name of Albert Einstein came along and changed everything. In 1905, Einstein published his theory of special relativity , which put forth a startling idea: There is no preferred frame of reference. Everything, even time, is relative.

Two important principles underpinned his theory. The first stated that the same laws of physics apply equally in all constantly moving frames of reference. The second said that the speed of light — about 186,000 miles per second (300,000 kilometers per second) — is constant and independent of the observer's motion or the source of light. According to Einstein, if Superman were to chase a light beam at half the speed of light, the beam would continue to move away from him at exactly the same speed [source: Stein , AMNH.org ].

These concepts seem deceptively simple, but they have some mind-bending implications. One of the biggest is represented by Einstein's famous equation, E = mc², where E is energy, m is mass and c is the speed of light.

According to this equation, mass and energy are the same physical entity and can be changed into each other. Because of this equivalence, the energy an object has due to its motion will increase its mass. In other words, the faster an object moves, the greater its mass. This only becomes noticeable when an object moves really quickly. If it moves at 10 percent the speed of light, for example, its mass will only be 0.5 percent more than normal. But if it moves at 90 percent the speed of light, its mass will double [source: LBL.gov ].

As an object approaches the speed of light, its mass rises precipitously. If an object tries to travel 186,000 miles per second, its mass becomes infinite, and so does the energy required to move it. For this reason, no normal object can travel as fast or faster than the speed of light.

That answers our question, but let's have a little fun and modify the question slightly.

Almost As Fast As the Speed of Light?

We covered the original question, but what if we tweaked it to say, "What if you traveled almost as fast as the speed of light?" In that case, you would experience some interesting effects. One famous result is something physicists call time dilation , which describes how time runs more slowly for objects moving very rapidly. If you flew on a rocket traveling 90 percent of light-speed, the passage of time for you would be halved. Your watch would advance only 10 minutes, while more than 20 minutes would pass for an Earthbound observer [source: May ]

You would also experience some strange visual consequences. One such consequence is called aberration , and it refers to how your entire field of view would shrink down to a tiny, tunnel-shaped "window" out in front of your spacecraft. This happens because photons (those exceedingly tiny packets of light) — even photons behind you — appear to come in from the forward direction.

In addition, you would notice an extreme Doppler effect , which would cause light waves from stars in front of you to crowd together, making the objects appear blue. Light waves from stars behind you would spread apart and appear red. The faster you go, the more extreme this phenomenon becomes until all visible light from stars in front of the spacecraft and stars to the rear become completely shifted out of the known visible spectrum (the colors humans can see). When these stars move out of your perceptible wavelength, they simply appear to fade to black or vanish against the background.

Of course, if you want to travel faster than a speeding photon, you'll need more than the same rocket technology we've been using for decades.

In a March 2021 paper published in the journal Classical and Quantum Gravity , astrophysicist Erik Lentz of the University of Göttingen in Germany proposed the idea of rearranging space-time to create a warp bubble, inside which a spacecraft might be able to travel at faster-than-light speeds.

Speed of Light FAQ

Is there anything faster than the speed of light, how fast is the speed of light in miles, why is "c" the speed of light, what is the speed of light on earth, lots more information, related articles.

• Data Sent via Infrared Light Could Make WiFi Hundreds of Times Faster
• How Light Propulsion Will Work
• How Light Works
• American Museum of Natural History. "A Matter of Time. " Amnh.org. (Feb. 16, 2022) https://www.amnh.org/exhibitions/einstein/time/a-matter-of-time
• Brandeker, Alexis. "What would a relativistic interstellar traveler see?" Usenet Physics FAQ. May 2002. (Feb. 16, 2022J) http://www.desy.de/user/projects/Physics/Relativity/SR/Spaceship/spaceship.html
• Carl Sagan's Cosmos. "Travels in Space and Time." YouTube. Video uploaded Nov. 27, 2006 (Feb. 16, 2022 ) https://www.youtube.com/watch?v=2t8hUaaZVJg
• Hawking, Stephen. "The Illustrated Brief History of Time. " Bantam. 1996. (Feb. 16. 2022) https://bit.ly/367UGpZ
• EurekAlert! "Breaking the warp barrier for faster-than-light travel. " Eurekalert.org. March 9, 2021. (Feb. 16, 2022) https://www.eurekalert.org/news-releases/642756
• Lawrence Berkeley National Laboratory. "Mass, Energy, the Speed of Light – It's Not Intuitive! " Lbl.gov. 1996. (Feb. 16, 2022) https://www2.lbl.gov/MicroWorlds/teachers/massenergy.pdf
• Lemonick, Michael D. "Will We Ever Travel at the Speed of Light?" Time. Apr. 10, 2000. (Feb. 16, 2022), 2011) http://content.time.com/time/subscriber/article/0,33009,996616,00.html
• May, Andrew. "What is time dilation? " LiveScience. Nov. 17, 2021. (Feb. 16, 2022) https://www.livescience.com/what-is-time-dilation
• NOVA Physics + Math. "Carl Sagan Ponders Time Travel." NOVA. Oct. 12, 1999. (Feb. 16, 2022) http://www.pbs.org/wgbh/nova/physics/Sagan-Time-Travel.html
• Ptak, Andy. "The Speed of Light in a Rocket." NASA's Imagine the Universe: Ask An Astrophysicist. Jan. 2, 1997. (Feb. 16, 2022) http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970102c.html
• Rynasiewicz, Robert, "Newton's Views on Space, Time, and Motion."Stanford Encyclopedia of Philosophy. Summer 2014. (Feb. 16, 2022) https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=newton-stm
• Stein, Vicky. "Einstein's Theory of Special Relativity. " Space.com. Sept. 20, 2021. (Feb. 16, 2022) https://www.space.com/36273-theory-special-relativity.html
• Van Zyl, Miezam (project editor)."Universe: The Definitive Visual Guide." Dorling Kindersley Limited. 2020. (Feb. 16, 2022) https://bit.ly/33q5Mpm.

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Will It Ever Be Possible To Travel Faster Than Light? This Is What The Science Says

At some point in our lives, we’ve all wondered if its possible to travel faster than the speed of light, just like how the Flash can move at ‘lightning’ speeds without working up a sweat. While modern physics deems this idea entirely impossible, there are some theories that suggest that some things in our universe may actually exceed the universal upper-speed limit.

In theory, it’s easy to ignore different factors such as air resistance or the effects of quantum mechanics on an object, but when talking about a real-life object, we have to take everything into account. For example, if two objects move from one place to another at the speed of light, the distance between them would increase faster as they are in motion. This all depends on what we consider to be the measure of speed of light and what medium the objects propagate in, not to mention the physics of space-time which is an entirely different and complicated topic to discuss right now. The speed of the objects also depends on what we consider to be the point of reference.

As explained in the video by Fermilab, the speed of light is different in different mediums. For example, if light enters a transparent medium like glass or water, it slows down while a charged particle would move with the same speed, hence appearing to move faster than light in that specific medium. So technically, we can say that some objects do travel faster than light under certain conditions.

While it’s still not possible to move a man-made object at the speed of light, many assumptions have been made regarding recent fundamental theories that shed new light on this topic, instead of rejecting the possibility of objects ever being able to travel faster than light, while not rejecting the laws of physics.

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Science: Can photons travel 'faster than light'?

By Marcus Chown

7 April 1990

LIGHT cannot travel faster than it does in a vacuum. This, at any rate, is what Einstein postulated in 1905. Now, however, a physicist in East Germany claims that photons may be able to break this universal speed limit, known as c. The proposed effect, however, is very small indeed: the photons can exceed Einstein’s limit by only one part in 10 36 .

K. Scharnhorst, of the Humboldt University in East Berlin, has made calculations using the theory of quantum electrodynamics, or QED, which describes how particles of light, or photons, interact with particles of matter – electrons and protons. His analysis of the vacuum, or empty space, reveals the possible existence of ‘faster-than-light’ photons (Physics Letters B, vol 236, p 354).

QED predicts that the vacuum, far from being empty, seethes with short-lived, or virtual particles: pairs of electrons and positrons – their antiparticles – which come into existence and disappear again for fleetingly small intervals. These are known as vacuum fluctuations (New Scientist, Science, 2 December 1989).

The apparent violation of the conservation of energy is permitted by Heisenberg’s uncertainty principle, a cornerstone of quantum theory. Before they disappear, an electron and positron may exchange a ‘virtual’ photon; alternatively, one of the particles may emit a ‘virtual’ photon, then promptly reabsorb it. These are known to physicists as ‘two-loop’ processes because the Feynman diagrams that represent them contain two loops (see Figure 1) .FIG-mg17112901.GIF

Scientists can observe the consequences of all these processes in the laboratory. One example is the Casimir effect, the result of a force that pulls together two closely-spaced metal plates.

Although in many circumstances photons behave as particles, they also have wave-like properties: in particular, they each have a wavelength associated with them. In effect, the plates exclude all virtual photons with wavelengths longer than twice the distance between the plates, technically because they do not satisfy the ‘boundary conditions’ imposed by the theory of electromagnetism. The imbalance causes the plates to be pushed together (see Figure 2) .FIG-mg17112902.GIF

Vacuum fluctuations also affect light as it travels through the vacuum. This is because, in flight, a tiny fraction of the photons spontaneously create virtual electron-positron pairs, which quickly annihilate each other to leave a photon. Two-loop processes also take place. All these contribute to the speed we measure for light in a vacuum.

Scharnhorst suggests that if the vacuum is modified, it may be possible to change the speed of light to more than its value in the vacuum. Such a modification can be brought about by bringing together two large conducting plates, as in the Casimir effect, and excluding some virtual photons.

This means that when photons travel between the plates, they cannot undergo two-loop processes that involve the excluded virtual photons. One would expect that the photons would spend a smaller fraction of their flight time undergoing two-loop processes than they would in a vacuum and so would travel marginally faster than they would in the vacuum.

In fact, detailed calculations are necessary to determine whether this is true. Scharnhorst has done the calculations and finds that it is. For photons travelling perpendicularly between plates separated by 1 micrometre, the speed of light is increased by about one part in 10 36 over its value in the vacuum. However, this effect is too small to be measured by any experiment.

Paul Davies of the University of Newcastle says that if photons could travel faster than the speed of light in a vacuum, it would have profound implications for physics. Many paradoxes would rear their ugly heads. In particular, events could violate ‘causality’; that is, an effect could occur before its cause. For this reason, he strongly suspects that the Universe will conspire to make Scharnhorst’s effect unobservable.

Davies says that in order to observe the effect, physicists would have to time a photon as it travelled across a short distance. They would have to measure as precisely as possible the time a photon is emitted by a source and then absorbed by a detector.

But atomic processes in the source and detector would be subject to Heisenberg’s uncertainty principle, which means there will be an uncertainty in both the time of emission and absorption. These uncertainties will be greater than the time interval physicists must measure in order to confirm Scharnhorst’s tiny increase in the speed of light.

One way to beat the uncertainty principle would be to use high energy photons, with correspondingly high-frequency. But then there is another problem, says Davies. The boundary conditions at the metal plates no longer apply at the energies required.

Davies concludes therefore that Scharnhorst’s result ‘does not imply the breakdown of causality’.

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Relatively Confused: Is It True That Nothing Can Exceed Light Speed?

POSTED BY Matt Strassler

ON 09/01/2022

A post for general readers:

Einstein’s relativity. Everybody’s heard of it, many have read about it, a few have learned some of it.  Journalists love to write about it.  It’s part of our culture; it’s always in the air, and has been for over a century.

Most of what’s in the air, though, is in the form of sound bites, partly true but often misleading.  Since Einstein’s view of relativity (even more than Galileo’s earlier one ) is inherently confusing, the sound bites turn a maze into a muddled morass.

For example, take the famous quip: “Nothing can go faster than the speed of light.”  (The speed of light is denoted “ c “, and is better described as the “cosmic speed limit”.) This quip is true, and it is false, because the word “nothing” is ambiguous, and so is the phrase “go faster”. 

What essential truth lies behind this sound bite?

Faster Than Light? An Example.

Let’s first see how it can lead us astray.

At the Large Hadron Collider [LHC], the world’s largest particle accelerator, protons collide with other protons. Just before a collision happens, a proton that has been accelerated to 99.999999% of c comes in from the right, and another accelerated to the same speed comes in from the left.

From your perspective, observing these two protons (using fancy electronics, not your eyes) from the LHC control room, the distance between the two protons is decreasing by almost the speed of light from the right and almost the speed of light from the left.  So it would seem that the distance between them is closing by almost twice the speed of light — by 1.99999998 c , if you want to be precise.  And if the distance between them is decreasing by almost twice the speed of light, then, well, their relative speed (as you see it) is faster than the speed of light.

That must be wrong, somehow, mustn’t it? Otherwise it would violate relativity… right?

But no.  It’s not wrong.  From your perspective, the two protons are approaching each other at nearly twice the speed of light.

Even simpler: point two laser pointers at one another, and turn them on at the same moment. The light beams will each be traveling at the speed of light, and the distance between them, from your perspective, will be decreasing at twice the speed of light.

When a flash of lightning occurs, light rushes off in all directions. The light moving north moves at c . The light moving south moves at c . From our perspective, standing on the ground, the distance between the light moving north and the light moving south grows at 2 c . That’s all there is to it.

But I thought — wait … — huh? — that can’t be ri … — didn’t Einst… ? — you’re full of… — I just don’t believe … — … …can’t be true!?! — well I [sound of head exploding.]

This is the kind of problem that sound bites lead to. Let’s take the two-proton example apart, and see what “nothing” and “go faster” actually mean.

The Can’t-Exceed-c Rule

What Einstein’s relativity actually says is this:

• From the perspective of any observer who measures the speeds of physical objects (using a careful laying out of aligned rulers for distance and synchronized clocks for time), no objects will ever be measured to be moving faster than the cosmic speed limit c , also known as “the speed of light in empty space.”

Let’s call this the can’t-exceed-c rule .  [This statement of the rule is okay as long as gravity isn’t too important; if gravity matters a lot, then it needs revision… which I’ll return to in a future post.]

The two protons individually don’t violate this rule: we, as observers in the LHC control room, view both of the colliding protons as moving slower than c.  And notice: the can’t-exceed-c rule says nothing about the relative speed of two objects as observed by a bystander.

But still, there is a potential threat to the rule lurking here. Suppose we somehow accelerated an observer (let’s name him Peter) to the same speed and direction as the proton coming from the left.  Peter would then move along with that proton, and would view it as stationary. From our perspective, as illustrated in Figure 1, we might think Peter would then view the proton from the right as approaching at nearly twice the speed of light.  That would violate the can’t-exceed-c rule.

Similarly, if Paula were traveling with the proton coming from the right, we might think she’d view the proton from the left as moving at nearly twice c .

Here’s where relativity of space and time as Einstein intuited it, and as experiments confirm, steps in to save the can’t-exceed-c rule. The point is this: because Peter is in motion relative to us, Peter’s view of space and time is not the same as ours. This is key. Because of his differing views, Peter will lay out clocks and rulers differently from how we, sitting in the LHC control room, would do so . Therefore, the way that Peter measures speed — the distance covered by a moving object over a certain amount of time — is different from how we are doing so. 

And that’s why, even though we measure the two protons approaching each other at nearly twice light speed, Peter will measure the right-moving proton approaching him below light speed. (The analogous statement would be true for Paula, traveling along with the other proton.)

In summary: from the perspective of an observer traveling with either proton, 

• we and the LHC control room are approaching at a speed of 0.99999999 c
• the other proton is approaching at a speed of 0.9999999999999998 c .

Meanwhile, from our perspective

• Both protons are approaching us (from opposite directions) at a speed of 0.99999999 c

Different observers simply disagree. Yet all are simultaneously correct. This is characteristic of things that are relative (i.e. perspective-dependent.) [You and I think the Sun is bright, but an observer out at Pluto would think the Sun is dim; there’s no logical contradiction, and all of us are correct.] The difference, again, stems from different (but equally valid) ways of measuring distances and durations.

[One thing we do have to agree on: if A views B as approaching with speed v, then B must also view A as approaching with speed v. Our perspective and those of Peter and Paula are indeed all consistent with this requirement.]

Notice that no one’s perspective violates the can’t-exceed-c rule. The universe preserves this rule, as described by the math of relativity, no matter how you try to trick it into an exception.  Yet that math doesn’t promise or assure that this rule applies to the “relative speed” of two objects — if “relative speed” is defined as the rate of change of the distance between two objects as measured by an bystander .

As always, though, definitions matter. If instead we defined the “relative speed” of two objects to be the speed of the second object as measured by an observer traveling with the first, or vice versa , independent of any bystander, then indeed that “relative speed” cannot exceed c. This is the definition implicitly used by physicists most of the time. But as with all definitions, it’s an arbitrary choice. It’s not the intuitive one most non-physicists would use.

From Sound Bite to Understanding

So what does “nothing can go faster than the speed of light” really mean?  “Nothing” means “No physical object”, and “Go Faster…” means “can be measured by an observer to be moving…” And altogether the sound bite means,

• “no physical object, from the perspective of any particular observer, can ever be measured to be moving faster than the speed of light in empty space, c .”

Even this comes with additional fine print. (The observer should be inertial and must make the measurement using an inertial frame of reference , and gravity had better be irrelevant; and I’ve left out some details about what “observer” really means and how the measurement is really made.) I’ll return to some of that fine print another time. But I hope it’s clearer now what the initial glib statement doesn’t mean.

Fundamentally, a sound bite or TL;DR approach to science can’t ever work. Many of the remarkable and non-intuitive features of the universe are within the grasp of non-scientists, but they require more than a single sentence, or even a paragraph. What sound bites do in relativity is similar to what they do in politics: they make us think we understand something, while actually obstructing the path to knowledge.

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36 Responses

The claiming that rela­tivity “sets aside the concept of energy” might not correct. As a static in extra space, the expansion is represented by “Red shift”, but in order to keep the speed (no expansion), the #Energy (frequency) is increased. ?

Pythagorean relativistic mechanics: That the Black body radiation possesses inertia was first pointed out by F. Hasenöhrl.” — Max Planck, 1909.

Radiation in a moving cavity. This case is of historic interest, since it can be treated by electrodynamics alone, even without relativity theory. Then one necessarily comes to ascribe momentum and thus inertial mass to the moving radiation energy. It’s interesting that this result was already found by F. Hasenöhrl before the introduction of relativity theory. However, his conclusions were in some points in need of correction. A complete solution of this problem was first given by K. v. Mosengeil.” — Wolfgang Pauli, 1921.

ADDENDUM: Equations for age gradient and moving-frame light velocities.

For all equations below, forward velocity is the z+ direction, xy is the transverse plane, and backward is z-.

Age gradient (or “timestamp slope”) using moving-frame z length (c-limited): a_g=-v/c^2

Relativistic age gradient across Lorentz-compressed rest z length (can go to infinity): a_γ = γ * a_g = -v / [c * sqrt(c^2 – v^2)]

Forward light-path length ratio R (moving-path over rest-path): R = sqrt((c+v)/(c-v))

Light velocity (positive) at angle theta from forward velocity z+: c_θ = c * R^(-cos θ) = c * [sqrt((c+v)/(c-v))]^(-cos θ)

Reciprocal light velocity (negative) at angle theta. Positive-negative product is c^2: c_θ = c * R^(cos θ) = c * [sqrt((c+v)/(c-v))]^(cos θ)

Forward (z+) light velocity: c_z+ = c_(θ=0) = c * sqrt((c-v)/(c+v))

Transverse plane (xy) light velocity: c_xy = c_(θ=π/2) = c

Backward (reverse, z-) light velocity: c_z- = c_(θ=π) = c * sqrt((c+v)/(c-v))

Matt Strassler wrote (September 1, 2022): > […] the speed of the second object as measured by an observer traveling with the first, or vice versa, independent of any bystander […] This is the definition implicitly used by physicists most of the time.

Indeed. In contrast, “the magnitude of the Galileian difference of the velocities of the two objects, as measured by a selected bystander” can be generally quite different from the (proper mutual) speed of the two objects wrt. each other; as well as generally quite different for different(ly selected) bystanders; except as far as the separate magnitudes of both velocities are both much smaller than “c”.

> But as with all definitions, it’s an arbitrary choice.

Since the definition of the one notion, or quantity, involves the selection, case by case, of a particular (and suitable) bystander, and the definition of the other does not, the latter is this much simpler, and in the jargon of physicists: “proper”.

Matt Strassler wrote (September 3, 2022 at 6:25 PM): > […] All motion in our universe is relative. […]

At least: “speed” is widely understood as “relative”; namely as being assertable “of one, in reference to another (suitable) one (with its suitable reference system)”. That’s a reason for not burdening the word “relative” with the task of distinguishing the names of differently defined notions of “speed”; i.e. for dismissing the suggested terminology “relative speed” in favor of “magnitude of Galileian velocity difference”, for instance.

Erratum: Delete next-to-last para, “The weird … sloppy, though.” (Grammarly is great, but it can’t catch everything.)

Hi Matt Strassler: I don’t think I can answer your most recent questions without explaining more precisely what I mean by “age gradients” since, at this point, I suspect there is no existing terminology for this idea after all. As usual, please feel free to truncate or delete this long answer as you see fit. Just so you know, I will post a copy of the content below on my website, regardless of whether you keep or delete it here.

———- Age gradients, a_g=-v/c^2, apply at all SR scales, including classical, so let’s forget particles for the moment and talk about human-scale clocks.

Picture two clocks, A and B, 100 m apart on the z-axis and linked by lasers [1]. What must one do to move this dual-clock system into the v_z = 0.6 c frame?

(1) Move B, the right-hand clock, 25 m left to create a new separation of 75 m. This movement — others are equally viable — presets the clocks to the 0.75 Lorentz factor for 0.6 c. Physical compression is required since each clock accelerates separately. If you don’t pre-compress, you get “frame ripping” along the z-axis (Bell’s string paradox).

(2) Reset the time on B by -200 ns. Why? Because the instant B starts moving at 0.6 c, light from A will take longer to reach it. Once accelerated, the B clock needs an extra 200 ns of “slack time” to let the light catch up. Without this spare time, it can no longer stay synch with A in the new frame.

(3) Wait if you want to. Contrary to what folks tend to assume, boosting is not mathematical magic. It’s an objective process with multiple steps, and you can do those steps in different ways with slightly different outcomes. I could, for example, have added 200 ns to A to create a different, but still fully SR-compliant, Lorentz transformation of the original system. The acceleration of complex objects is quite a messy process.

(4) Accelerate both clocks “instantly” to 0.6 c in the z+ direction. It is only then that the boost abstraction — the mathematical abstraction that there is a self-existent “space” for understanding how the system behaves — even kicks in. Without prep steps 1 (Lorentz contraction) and 2 (application of the age -v/c^2 age gradient), you don’t get a _self-consistent_ Lorentz transformation of the original system.

The age gradient — the smooth -v/c^2 gradient one must add to transform a system correctly from one frame to another — is a separate feature of frame transformation. Just as you must pre-compress length to prevent “space ripping” (Bell’s string paradox), you must also pre-adjust clock settings to avoid “time ripping” of the object in the new frame, that is, to keep it in sync with itself. Ensuring time dilation is a _dynamic_ effect of a different sort. That’s why you can, if you wish, insert the “wait a bit” step 3 after finishing steps 1 and 2. In sharp contrast, if you don’t pair and correlate the Lorentz contraction and “age-sloping” transformations, you end up with an inconsistent result.

Age gradients are part of converting twin-type paradoxes into fixed, non-relative rates within the most recent launch frame that encompasses all of the interacting structures. There’s also a launch-frame energy hierarchy.

Does any of this affect quantum, though?

Yes. In particular, the complex-plane phases of Schrodinger momentum wave functions are age gradients. Rest-mass quantum frequencies acquire age gradients in the direction of motion, twisting their amplitudes into a helix.

I’m sorry if I’m introducing new physics in any or all of this. I was sincere when I said I’m just trying to figure out the names of some of this stuff. When I find something interesting — Glashow’s cube is an example — I assume it’s well-known, and I don’t yet know the right keywords to look it up.

But if there are no existing keywords, then maybe it is new. But why would such an almost absurdly simple concept get overlooked for over a century?

Increasingly, I suspect it’s because the Poincare symmetries work so well that the instant we say “object,” our brains switch over to moving-frame space and time. Why not? They are, after all, absolutely valid coordinates. Thus the fact that we changed frames doesn’t even occur to us.

The danger of that seductive little mental flips is that it undermines how fiercely SR applies in every situation. SR applies even ones when it converts ordinary into weirdly sloped time entities whose dynamics are better modeled by making the speed of light reciprocal in the forward (c/R) and backward (Rc) directions. (I know there are papers on that, but they use 1/2 c and infinity, and that’s just wrong; space is always relative.)

The weird and very non-real. That’s wrong, but it makes it tempting to mentally switch back to the moving frame instead of entirely forcing the systems into the rest frame. That’s a bit sloppy, though.

———- [1] The two-clock system details are: Both clocks use Doppler to stay at rest relative to the other. Both use 667 ns (200 m / c) send-return signal loops to ensure 100 m separation. Both send their current times in each send-return loop, and both synchronize their clocks based on the other clock being 333.6 ns distant.

I mentioned a number of quantities in the above comment, all of which have precise definitions. I’m not sure whether Matt Strassler’s new spam filter will accept text-form equations, since they resemble code and could easily trigger a generic exclusion in an untrained filter. I’ll give it a try after this test comment, though most likely, that would also get me banned from posting.

I’ve never heard of someone contemplating the relative speeds in relation to the cosmic speed limit. (But maybe I’m too stuck with the relativistic physics.) So this was a hard example to retcon the intended wrong formulation out of.

Sure, it reminds of astronomical observations of angular speeds, where you have to be careful since appearances deceive. (Or in terms of the example, rotate a laser pointer and observe the spot “speed” on a distant wall exceed the cosmic speed limit.)

The issues of astronomical observations of angular speeds is a little different, but equally important, since it has to do not with *measured speeds* but with *apparent speeds* (where light travel time has not been accounted for.) Another case I plan to write about.

As for today’s case: I know I’ve been asked about this puzzle at least a dozen times by non-experts, so it must be a pretty common confusion.

Another great write up. If I could ask a question, with a slight modification to your scenario. I’m in my space ship, initially at rest relative to a distant star. I see the light from that star coming to me at the speed of light, and a certain “color” (frequency). I then accelerate to .999999 the speed of light, relative to that star. I would still see the light from that star approaching me at C, but wouldn’t it be frequency shifted? If so, as the light shifts frequency, as my velocity relative to the star was increasing, wouldn’t the frequency eventually shift into the ultraviolet and I wouldn’t be able to see the star anymore? Wouldn’t those high energy UV photons (or higher) start doing damage to me and my ship?

Yes, the light would be blueshifted, would become invisible to your eyes (though not a UV light detector), and would become dangerous. Effects like this are widespread in cosmic ray physics, where the collision of a ultra-high-energy cosmic ray with some poor unsuspecting slow particle can create a dramatic effect; examples are cosmic ray proton (say, 1 PeV) + microwave photon from the cosmic microwave background (0.001 eV) can lead to proton + newly created electron + positron, which a microwave photon normally couldn’t do. There are lots of other examples, such as https://cerncourier.com/a/cosmic-ray-particles-could-give-information-about-neutrino-mass/ .

Incidentally the reason James Webb telescope aims at infrared light is that starlight from distant galaxies has been redshifted (by the universe’s expansion) to the point that our eyes can’t see it. It’s a real effect.

I don’t understand. The whole article is about relative motion and measuring relative motion. Two cars moving in opposite directions one with 30 km, the other with 70 km, will measure 100 km relative to each other. This does not mean that either of the car is moving with 100 km. Why would this be any different for the speed of light.

“This does not mean that either of the car is moving with 100 km. ” Yes it does. ***All motion in our universe is relative.*** If someone in the first car measures the second car to be moving at 100km/hr, then yes, that’s its speed (in the reference frame of the first car, which is just as good and just as bad as the reference frame centered on the ground.)

From the Sun’s point of view, both cars are moving at several km/second. Are you saying the Sun is wrong?

Matt, have you ever browsed the Google newsgroup sci.physics.relativity?

I ask because relative velocity, closing velocity etc is what many skeptics there believe contradicts special relativity, and your post gets to the heart of their confusion precisely and quickly IMO. There’s also the experimental evidence for relativistic kinetic energy which even the most hardened skeptic finds difficult to refute: The velocity of an object approaches a limiting c, yet the temperature of the stationary target it collides with continues to increase unbounded as shown by experiments around the world.

“Peter will lay out clocks and rulers differently from how we, sitting in the LHC control room, would do so”. Yes, that’s the crucial point for me or equivalently: “Peter will label the same event point using his clocks and rulers differently…”

In every day life we can see this in the case of the labeling of space coordinates and their corresponding differences by comparing how a driver in a car will do this compared to someone on a road using their rulers. It’s something we take for granted. Then Einstein came along and claimed this was symmetrically also true for the labeling of time coordinates for events in a way that maintained a constant universal speed limit c for all observers.

No, I haven’t. Experimental evidence for relativistic kinetic energy is also completely obvious at the Large Hadron Collider, which wouldn’t work without it; the whole principle of the the machine is based on it, and it all has to be timed with extreme precision, requiring precise knowledge of the speeds involved. The protons move at nearly the speed of light, but bunches collide over a tiny fraction of a nanosecond, and do so every 25 nanoseconds, while traveling around a tunnel 27 km (i.e. 90 microseconds) long, and they do so for hours. There’s no wiggle room to mess with basic relativity in such a system — so anyone who doesn’t understand this is spouting silliness.

“No matter how fast the light is” (Pendapat Saya 🙂

spontaneous is faster than light…

Lorentz transformations work because they project four-dimensional structures into an observer’s xyz space. But there’s more structure to such projections.

Would you happen to know the standard name for the age gradient — my phrase, sorry — that accompanies Lorentz compression?

It maxes out at sbout -3.34 ns/m and makes the front end of your LHC proton 2.78 × 10^(-24) seconds younger than the back end.

Also, is there a name for the relativistic version of this age gradient, which for high-gamma objects is gamma*(-3.34 ns/m)?

I’ve tried to look this up but had no luck.

You are implicitly assuming something about how you are measuring age; how was the proton born?

All you are really doing is measuring the time it takes for light to travel from one side of the proton to the other.

If you image a proton at rest you see quark positions guided by conservation rules. If you image the same proton at 0.99 c, you see its trailing quarks in slightly retarded positions relative to the expected pattern.

Watching a sequence of such images would be like watching a movie where the left side of each frame is a half second older than the right side. How the proton was created should not matter.

As you aptly noted, lightspeed delays are the root cause of retarded quark positions. But if Lorentz contraction is experimentally real and measurable, then trailing-side quark-position retardation should be just as real, since they are part of the same 4D-to-3D projection package.

Erratum: _Advanced,_ not retarded. Rest views clocks at the trailing edge of a moving object as _ahead_ of clocks in its leading edge. The age gradient a_g = -v / c^2. Apologies for any confusion. (I should read my own papers.)

I’m still not clear what your question is. Are you asking about wave functions of objects in motion? We don’t need to worry about something as complicated as a proton. Why don’t you think carefully about the properties of a boosted hydrogen atom or positronium (but be careful, because you need to account for virtual photon emission from the electron, as well as virtual electron-positron pairs; you are treating it as a relativistic system, after all.)

Please see the main thread for my (long) response.

Or more simply: no it is not true, things can move faster than light in a medium.

While this is a true statement, do you really think it’s more important than saying, “yes, it is true, as long as you mean ‘the speed of light in empty space, c.’ ” ? That is, is “no” really more profound, and more insightful, than “yes” with proper definitions? I don’t buy it. There’s almost nothing more important in physics than local causality, which is the formal way of saying “yes”.

It is possible to travel faster than the speed of light, but to explain how, I need to introduce some basic field structuring and fourth vector structuring concepts. [Extended nonsense removed by host.]

Cherenkov radiation came to mind with the title on this one.

Regardless, I think the point of Relativity is lost when comparing “speeds” based in simultaneity from one’s own perspective. Events separated in space are not simultaneous in different frames, and an observer of two separated events is simply subject to the interpretations of what can be observed from her own frame… in this case, a near twice light-speed rate of closure from a central perspective of one comparing information arriving from two disparate light cones.

What is preserved from any perspective is *causality* (and retro-causality?). As you point out, Relativity implies that the way any observer measures both time and distance from their own frame will always insure that no one breaks the rules… but fundamentally such that from any perspective the protons reach the same point and collide *before* resulting in a spectacular spray of particles.

I think the more interesting question is what this means when we venture to follow the light cones backward as far as we can?

You’re thinking like a physicist. You know too much. Cherenkov radiation is the least of the conceptual problems with relativity, if you’re not a physicist.

As you say, a better way to view relativity is through causality, whose structure arises at space-time points. In the absence of gravity (and thus space-time curvature) we can however, extend our understanding from a single point across all of spacetime, if we have a consistent frame of reference. I’m not sure what you mean about comparing speeds “based in simultaneity from one’s own perspective.” In the absence of gravity, speeds of objects at different locations can be compared… and this is true in virtually all particle and atomic and molecular processes on Earth, since gravitational effects are very, very slow.

Is there another caveat needed for things that can reduce the vacuum index of refraction to slightly less than 1, thus slightly increasing the speed of light moving between two Casimir plates to a bit more than c? Of course, this effect would be so ridiculously tiny that I don’t see how it could ever be measured.

I don’t know if “caveat” is the right word so much as a “caution” to again read the fine print very, very carefully. Relativity constrains physical objects and information. Index of refraction less than one affects parts of waves, but still doesn’t allow photons — objects — to exceed c. In https://en.wikipedia.org/wiki/Refractive_index there’s some discussion of refractive index below unity.

In the LHC, lead nuclei Lev and Dex approach each at equal and opposite near-c velocities. They appear in the CMS detector as Lorentz-compressed oblate spheres with similar thicknesses that merge to form a single excited oblate sphere in the CMS rest frame.

The rightmost nucleons of Lev and leftmost nucleons of Dex collide first, initiating the formation of quark-gluon plasma in the CMS frame… [Abridged by editor since it had an error and was quite long.]

So, three questions:

(1) Which of these historically incompatible models is correct?

(2) Which one does CERN use?

I think this is more complicated than necessary. You can ask the same thing of proton-proton collisions: how do you describe the collision in the lab frame, in one proton frame, or in the other proton frame? You can do any one of the three, it’s just a translation of the physics from one perspective to another, if you do it correctly. But the easiest one for LHC-relevant phenomena is the lab frame in which both protons are flattened into pancakes by length contraction. The same is true for heavy ion collisions. So (1) all three are correct, they are not historically incompatible — cause and effect work perfectly in all descriptions, thanks to relativity; (2) scientists use mostly the lab frame where both nuclei are pancakes, and (3) they do so because experience shows this is easier, partly because protons and neutrons are simpler when fast-moving than when at rest, but not because there’s

Yep! The bogus part of my thought experiment was simple in retrospect: In the nuclei views, I kept the plasma moving at the _same_ velocity as that of the other nucleus creating it. It doesn’t, of course. It slows down just enough to match the CMS frame view of a plasma at rest.

Had I done the transforms _before_ jumping to imagery, the deceleration of the plasma would have showed up trivially. All I did was build a bogus and deceptive visual image. Wow!

Again, thanks.

Speed is the distance covered in Space at a period, if it is SpaceTime, Space itself adjust to the time. If it is more Space light has to travel more speed to Cover the speed “c”… or as a paradox, create a curve, that what we call the “mass”?

The claiming that rela­tivity “sets aside the concept of energy” might not correct. As a static in extra space, the expansion is represented by “Red shift”, but in order to keep the speed (no expansion), the #Energy (frequency) is increased.

Without ‘relativity’ we cannot get the “Moon and Sun” at the same size (even by excluding the Parallax libration). This “Time dilation” is the physical reality, where ironically we get the ‘Rest mass’, not a physical reality but only a Mathematical “zeta value”. Riemann laid the foundations of the mathematics of general relativity.

Srinivasa Ramanujan under Godfrey H. Hardy worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he found a value for the sum of such series using a technique he invented that came to be called Ramanujan summation. “The study of Euler’s works will remain the best school for the different fields of mathematics and nothing else can replace it.”- Carl Friedrich Gauss. The existence of “Closed forms for polynomial roots (probability density)” hinted “at lowest Energy the Energy Limit itself as a Equation to Matter (not the Mass at first)”, equates Space & Time to SpaceTime. Linear Regression analysis was conducted to establish the correlation between global and cartesian planimetric coordinates of and regression models generate results in GPS (Geodesy).

The thought of St. Augustine of Hippo revolved around dualisms, inheritance of Plato and Oriental Manicheans, brought the belief Systems to #Holographic (2D), like Pythagorean and Cartesian coordinate system by Soma or Surā.

But in egyptian Amun or Amen (truth?) , god of the air (2D phonon or Soma), the left side has Female symbol ♀️ and the cone head tilted to female side, depict the anti-gravity tree growth pulled to “lowest #Energy”, called the Mass.

Figure 2 confuses me. It would seem to be a totally different case than Figure 1. With Figure 1 the left proton moves at 0.9999999c and Figure 2 showing 0.999999999998c. I would think an observer accelerated to the same speed as the traveling proton would view it a stationary and the the article says so. “…would view it as stationary” Then the 0.9999999998 shows up in Figure 2.

I took it to mean the Figure 1 and 2 were the same case from a different perspective but I guess only “consistent” was meant. “That this picture can be consistent with Figure 1”

Or maybe I am missing something here.

Hmm — Are you confusing “from the left” with “to the left”? I’m trying to see where I might have flipped one with the other in my text, but can’t find an error. The statement was that Peter (drawn on the left of Figure 2) is stationary with respect to the proton coming *from the left*, and sees the proton coming *from the right* as moving at 0.999999999998c .

If there’s something inconsistent in my text let me know, but as far as I can see you’ve flipped left and right in the situation I’ve described in the text.

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