A Catholic Citizen in America

It’s been 30 years since a Mexican theoretical physicist said that a warp drive was possible: hypothetically. And published math that backed up his claim.

Last month, a team of scientists showed how we could build a warp drive: again, with math backing up their claim.

This year’s variation on the Alcubierre drive couldn’t travel faster than light. But it can, they say, be built with materials we have today.

This is a very big deal. And it’s what I’m talking about this week. Along with whatever else comes to mind.

• Speed of Light, Math, and Approaching Infinity
• New “Warp Drive” Approach: This One is Testable
  • Gravity, Newton’s Law, Einstein’s Math, and — Negative Mass?
  • Math, My Father, and Me: A Digression
  • “Exotic Solutions” Offering a “Novel Means of Transportation”
  • A Testable Warp Solution: Exciting!
• The Day “Warp Field Mechanics 101” Disappeared
• History —
  • — And Being Human

Speed of Light, Math, and Approaching Infinity

First of all, we can’t make a vehicle travel faster than light. Not now. Not with any propulsion technology that’s even remotely conventional. And maybe not ever.

The ‘light barrier’ isn’t like the sound barrier — although both involve equations that give answers approaching infinity when approaching the phenomenon’s speed.

Early, very simple, math describing airfoil drag as a function of speed showed that drag became infinite at the speed of sound. According to those early equations.

But scientists had been studying things that travel faster than sound, like meteorites.

And they’d occasionally fire experimental airfoils at supersonic speeds. Which helped them develop more accurate mathematical models. So they knew that accelerating something beyond the speed of sound was possible.

“Breaking the sound barrier” was mainly an engineering issue.

The ‘light barrier’, on the other hand, involves how matter and energy work in this universe.

In physics, momentum is the form of energy an object has due to its motion. The faster it goes, the more energy it has; and the more massive it is — but that’s an angle of relativity I’ll leave for another time.

Newton’s math is an excellent model for objects that are traveling at tiny fractions of the speed of light.

As we pump more energy into an object, making it go faster, though, things get interesting. As an object approaches speed of light, its momentum approaches infinity. For anything that has a rest mass greater than zero, that’s not possible.

This increase in mass was detected at least by 1901.

Since then, increasingly accurate tests of relativistic mass increase have confirmed that this universe does, in fact, have a speed limit.¹

New “Warp Drive” Approach: This One is Testable

The metric creation method outlined above is from the “warp drive” research paper published last month. I’ll be talking about what they found, but not the math.

First, though, I’ll share what a scientist had to say.

Paul Sutter, physicist and “science communicator”, did a pretty good job of discussing this latest analysis of a “warp drive”.

I’m not overly fond of the “warp drive” moniker. But the idea, and the name, got traction with Alcubierre’s “LETTER TO THE EDITOR: The warp drive: hyper-fast travel within general relativity”.² (Classical and Quantum Gravity, 1994)

“New warp drive concept does twist space, doesn’t move us very fast”
“While it won’t make a useful spaceship engine, it may tell us more about relativity.”
Paul Sutter, Ars Technica (May 23, 2024)

“…Einstein’s general theory of relativity is a toolkit for solving problems involving gravity that connects mass and energy with deformations in spacetime. In turn, those spacetime deformations instruct the mass and energy how to move. In almost all cases, physicists use the equations of relativity to figure out how a particular combination of objects will move. They have some physical scenario, like a planet orbiting a star or two black holes colliding, and they ask how those objects deform spacetime and what the subsequent evolution of the system should be.

“But it’s also possible to run Einstein’s math in reverse by imagining some desired motion and asking what kind of spacetime deformation can make it possible. This is how the Mexican physicist Miguel Alcubierre discovered the physical basis for a warp drive—long a staple of the Star Trek franchise….”

“…While tantalizing, Alcubierre’s design has a fatal flaw. To provide the necessary distortions of spacetime, the spacecraft must contain some form of exotic matter, typically regarded as matter with negative mass. Negative mass has some conceptual problems that seem to defy our understanding of physics, like the possibility that if you kick a ball that weighs negative 5 kilograms, it will go flying backwards, violating conservation of momentum. Plus, nobody has ever seen any object with negative mass existing in the real Universe, ever….”

“…But there is a way around it, discovered by an international team of physicists led by Jared Fuchs at the University of Alabama in Huntsville. (The team is also affiliated with the Applied Propulsion Laboratory of Applied Physics, a virtual think tank dedicated to the research of, among many other things, warp drives.) In a paper accepted for publication in the journal Classical and Quantum Gravity, the researchers dug deep into relativity to explore if any version of a warp drive could work….”
[emphasis mine]

Gravity, Newton’s Law, Einstein’s Math, and — Negative Mass?

Backing up a bit, gravity is a very basic part of this universe.

Describing it as a force, as Newton’s law of universal gravitation did, works very well for stuff that’s standing still or moving at tiny fractions of the speed of light.

Scientific laws, by the way, aren’t like laws written in the United States Code.

They’re regularities scientists have noticed, studied, and described. These descriptions, in turn, let scientists predict what will happen in given situations.

Predicting what will happen sounds a bit like divination. Saul tried something of the sort, getting a postmortem interview with Samuel. (1 Samuel 28:7–25) That was a bad idea. So is divination. (Catechism of the Catholic Church, 2115-2117)

But noticing how this universe works, and using that knowledge, is part of being human. It’s what we’re supposed to do. Ethics matter, the same as any other part of our lives, and that’s another topic. (Catechism, 2293-2295)

One more thing, before getting back to my last excerpt from Paul Sutter’s article.

He said that negative mass has never been observed. He’s right about that.

In this context, negative mass is a part of space which has, for some observers, a negative mass density.

Maybe that’s physically impossible.

But the condition fits Einstein’s math.³

“…Us physicists like it when all of our theories line up and agree on the nature of the Universe. So if the energy conditions set real limits on physics—limits where things like negative mass don’t just not exist, but can’t exist—then we’d like a physical theory that says that from the beginning, instead of relying on add ons like the energy conditions.

“Exploring how a warp drive might (not) work, and under what conditions and restrictions, is a step in that direction. For years physicists thought that the energy conditions outlawed all kinds of warp drives, yet the new research shows a possible way around that. What comes next will be a win no matter what; whether we get a fancy superluminal warp drive or not. That’s because whatever comes out of future lines of inquiry along these directions, we’re going to learn more about the force of gravity, and just possibly revolutionize our understanding of it.

“And who knows what we’ll get once we understand gravity better.”
“New warp drive concept…“, Paul Sutter, Ars Technica (May 23, 2024) [emphasis mine]

Math, My Father, and Me: A Digression

Much as I’d like to explain how those equations work, I can’t. Which is doubly frustrating, since I enjoy understanding stuff and sharing what I’ve learned — and those standardized tests in high school said I should be good at math.

Maybe so, but I’m guessing that I’m a lot like my father that way.

He told about one question in a calculus test he took. It was partly multiple choice: describing two cylinders, asking for the volume they shared, with five possible answers.

My father did what I would have done. He looked at the two cylinders with his mind’s eye, saw how much space their intersection occupied, and checked off the answer that matched that quantity. Then he tried filling in the “show your work” part of the question.

My father’s equations were garbage. But he was the only one in the class to check off the correct quantity.

He and I emphatically have not lived with aphantasia. That’s not being able to form mental images: first described in 1880 and pretty much ignored ever since. Although I gather there’s been an uptick in interest, and I’m wandering off-topic.⁴

My experience with calculus was less noteworthy.

I took, but didn’t pass, a calculus class. A couple times I got that familiar ‘aha!’ moment, when ideas fall into place. But each time that happened, my attention flickered — and the ‘aha’ was lost without a trace. Frustrating.

“Exotic Solutions” Offering a “Novel Means of Transportation”

That won’t keep me from talking about what scientists do, since I can read what they say about their math.

“Constant Velocity Physical Warp Drive Solution”
Jared Fuchs, Christopher Helmerich, Alexey Bobrick, Luke Sellers, Brandon Melcher, Gianni Martire; preprint draft (May 4, 2024) via arXiv, Cornell University

“Abstract
“Warp drives are exotic solutions of general relativity that offer novel means of transportation. In this study, we present a solution for a constant-velocity subluminal warp drive that satisfies all of the energy conditions. The solution involves combining a stable matter shell with a shift vector distribution that closely matches well-known warp drive solutions such as the Alcubierre metric. We generate the spacetime metric numerically, evaluate the energy conditions, and confirm that the shift vector distribution cannot be reduced to a coordinate transformation. This study demonstrates that classic warp drive spacetimes can be made to satisfy the energy conditions by adding a regular matter shell with a positive ADM mass.”

Before I move on, a few definitions. ADM mass involves energy, and metric tensors is geek-speak for describing a space-time. I’ve put links in the footnotes.⁵

“In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past….”
(Metric tensor (general relativity)) [emphasis mine]

A Testable Warp Solution: Exciting!

“Conclusion
“…This exciting new result offers an important first step toward understanding what makes physical warp solutions. Moreover, the warp drive spacetime constructed here is a new type of warp drive beyond the Natario class and hence not subject to the same scope discussed in [9] and [18] due to its use of modified spatial terms in the metric. This new solution shows that a more generic constant velocity warp drive spacetime can be constructed that satisfies the energy conditions.

“We intend to explore this solution further and find areas of optimization to improve the mass-to-velocity ratio required to maintain physicality….”
(“Constant Velocity Physical Warp Drive Solution“; Jared Fuchs, Christopher Helmerich, Alexey Bobrick, Luke Sellers, Brandon Melcher, Gianni Martire; preprint draft (May 4, 2024) via arXiv, Cornell University)

“Excited” pretty well sums up my reaction to this research. That’s not a common response. Not these days, not to this extent.

I graduated from high school shortly before the Apollo 11 landing. There’ve been quite few “exciting” events since then.

But this? For me, this is the biggest thing since I ran across “Warp Field Mechanics 101” on the NASA website: and the next day NASA (apparently) ‘went black’. I’ll talk about that a little later.

I do not think this means we’ll soon have fast interplanetary travel. Even though the scientists mention “exotic solutions” offering “novel means of transportation” and “passengers”.

“…1.2 Designing Warp Drive Spacetimes
“The transportation element of warp drives is about designing timelike curves for passengers to travel between points A and B in spacetime. In this paper, we will go about developing a warp solution in the following steps….”
(“Constant Velocity Physical Warp Drive Solution“; Jared Fuchs, Christopher Helmerich, Alexey Bobrick, Luke Sellers, Brandon Melcher, Gianni Martire; preprint draft (May 4, 2024) via arXiv, Cornell University)

What’s genuinely fascinating here is that their ideas can be tested, using light sources, detectors, mirrors, and a “stable shell of matter”: ordinary matter. Nothing exotic or hypothetical.

The only other example of practical “warp drive” laboratory test equipment I’ve run across is the 2011 White-Juday warp field interferometer.

The last I heard, the White-Juday warp field interferometer gave inconclusive results. If it generated space-time distortions, they could have been masked by electronic noise and ionized air.⁶

What astonished me about the White-Juday warp field interferometer was that scientists thought there was even a remote chance of (1) generating detectable space-time distortions (2) with contemporary technology.

This year’s revisiting of “warp drive” physics may also yield inconclusive results.

But — and I think this is important — these scientists outlined how others could test their ideas: and said they “intend to explore this solution further”.

No matter how the tests come out, we’ll be learning more about how space-time works.

Then, as Paul Sutter said, “…who knows what we’ll get once we understand gravity better.”

The Day “Warp Field Mechanics 101” Disappeared

A little over 11 years back, I felt as if I’d dropped into a science fiction thriller. Briefly.

…March 18, 2013. I’d been looking through NASA’s discussions of ‘next generation’ and ‘beyond next generation’ propulsion technology.

Two documents caught my eye:

• “Warp Field Mechanics 101”
  Dr. Harold “Sonny” White, NASA Johnson Space Center (2011)
  (from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492_2011024705.pdf (March 18, 2013))
• “Eagleworks Laboratories: Advanced Propulsion Physics Research”
  Dr. Harold “Sonny” White, Paul March, Nehemiah Williams, William O’Neill; NASA Johnson Space Center (2011)
  (from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf (March 18, 2013))

My habits include downloading information for later study.

Usually it’s not necessary. This time it was.

March 19, 2013. I went back to the NASA website.

NASA wasn’t there. Apart from a few polite statements that data was not available.

NASA had gone black.

Classic Science Fiction Thriller (or) Another SNAFU

I’ve read enough stories to recognize a classic science fiction thriller plot.

But I was pretty sure that folks at NASA hadn’t inadvertently leaked Top Secret Stardrive Documents. Cool as that might have been.

As it turns out, someone had hacked into United States government databases.

Information Technology folks couldn’t tell exactly how much had been accessed.

Someone higher in the administrative food chain realized that at least some of the compromised data shouldn’t be shared with everyone. And so the whole NASA website went offline. Along with other U.S. government sites….

NASA eventually came back online, I stayed interested in “warp drive” research, and I talked about NASA ‘going black’ in 2013:

• “Social Media, Security and Assumptions” (February 6, 2021)
  • When NASA ‘Went Black’

I didn’t find any references to the March, 2013, hacking incident then. I did this week: but only two. And I’m not sure about a 2018 reference to “an attack in 2013”.⁷

Anyway, I said I’d talk about the day NASA ‘went black’, and I still think it’s a good story.

History —

History doesn’t repeat itself. Not exactly.

But I’ve noticed that patterns to recur.

So I could note that Konstantin Tsiolkovsky published his rocket equation in 1903, Robert H. Goddard launched the first liquid fueled rocket in 1926, and Apollo 11 landed on the Moon in 1969.

Then I could say that, since it was 23 years since Alcubierre first published his math, someone flight-tested a warp drive in 2017.

And that the first interstellar ship with a warp drive will reach Alpha Centauri in 2060: 43 years after the 2017 flight test, just like Goddard and Apollo.

I could, but I won’t. Paul Sutter was right. Variations on the Alcubierre drive would need something like dark matter. And nobody has observed such a thing. Not directly.

Einstein’s math suggests that dark matter could, hypothetically, exist. And if it does, then it explains oddities like the orbits of stars in spiral galaxies.

But even if it’s real, we’re not even close to manufacturing or collecting the stuff, let alone using it in a propulsion system.

I suspect a closer analog to Alcubierre’s 1994 letter to the editor might be William Moore’s “On the Motion of Rockets both in Nonresisting and Resisting Mediums”. (1810)

That paper wasn’t exactly lost, but it wasn’t widely available either.

So about a century later, Tsiolkovsky, Goddard, and Hermann Oberth came up with pretty much the same results. Independently.⁸ Which shouldn’t be surprising, since all four scientists were studying the same universe.

— And Being Human

One thing of the many that had changed, a century after William Moore’s research, was that technology was starting to catch up with the math.⁹ Awkward metaphor, but it’s Friday afternoon and I’ll let it stand.

Again, history doesn’t repeat itself: but I’ve noticed the occasional pattern emerge from humanity’s long story.

One thing that hasn’t changed in the uncounted ages before we started keeping written records is our wondering what’s over the next hill. We’re now living on every one of Earth’s continents; although I’ll grant that our Antarctic settlements are more camps than towns.

Even if something drastic happens in the next few decades, I’d be astounded if we don’t eventually get around to revisiting the Moon — following our robots to Mars — and finding a way of reaching the stars.

I’ve also noticed that at least some theoretical physicists have gone from saying that a warp drive is impossible — to showing ways it might work, once we develop the technology. And find something that’ll work like dark matter would.

Maybe — a century, or a millennium, from now — we’ll learn how to build warp drives.

Or maybe we’ll learn that there isn’t a fast way to the stars.

Either way, I think that’s where we’re headed.

I’ve talked about this sort of thing before:

• “Double Jupiters, a JuMBO Puzzle; Antimatter Falls Down”
  (October 7, 2023)
• “Fusion Rocket Engines, SETI and Science: Seriously”
  (July 29, 2023)
• “TAE and ITER: A Few Steps Closer to Fusion Power”
  (May 21, 2022)
• “Fusion Rocket Engines, SETI and Science: Seriously”
  (July 29, 2023)
• “‘One Small Step’ in a Long Journey”
  (July 20, 2019)

¹ Sound, light, physics, and technology:

• Wikipedia
  • Bell X-1 (origional designation originally as the XS-1, first aircraft to exceed speed of sound in level flight. (1948))
  • Faster-than-light
  • General relativity
  • Kinetic energy
  • Mass in general relativity
  • Momentum
  • Newton’s laws of motion
  • Speed of sound
  • Sound barrier
  • Special relativity
  • Speed of light
  • Tests of relativistic energy and momentum
  • Velocity

² Alcubierre’s letter to the editor and paper, 1994 and 2000? I haven’t learned the story behind that/those:

• Wikipedia
  • Paul M. Sutter
  • Science communication
• “Constant velocity physical warp drive solution“
  Fuchs, Jared; Helmerich, Christopher; Bobrick, Alexey; Sellers, Luke; Melcher, Brandon; Martire, Gianni: Classical and Quantum Gravity (May 2024) abstract, NASA/ADS (Harvard)
• “Constant Velocity Physical Warp Drive Solution“
  Jared Fuchs, Christopher Helmerich, Alexey Bobrick, Luke Sellers, Brandon Melcher, Gianni Martire; preprint draft (May 4, 2024) via arXiv, Cornell University
• “The Warp Drive: Hyper-fast Travel Within General Relativity“
  Miguel Alcubierre; preprint draft (submitted September 5, 2000) published in Classical and Quantum Gravity, IOP Publishing (September 2000) via arXiv, Cornell University
• “LETTER TO THE EDITOR: The warp drive: hyper-fast travel within general relativity“
  Miguel Alcubierre; abstract; Classical and Quantum Gravity, Volume 11, Issue 5, pp. L73-L77 (May 1994) via ads (astrophysics data system), Harvard

³ Mostly recent science, with a glance back at where we’ve been:

• Wikipedia
  • Astrophysics
  • Gravitational wave
  • Gravity
  • Introduction to general relativity
  • Modern physics
  • Natural philosophy (we started calling in “science” a few centuries back)
  • Negative mass
  • Newton’s law of universal gravitation
  • Newton’s laws of motion
  • Scientific law
  • Spacetime
  • Thales of Miletus (natural philosopher, late seventh and early sixth century B.C.)
  • United States Code

⁴ Mental imagery and a little math:

• Wikipedia
  • Aphantasia (having no mental imagery)
  • Calculus
  • Hyperphantasia (having extremely vivid mental imagery)
  • Prefrontal synthesis
  • Standardized test (“This article may require copy editing for Writing becomes slightly informal and essay-like in some sections….”)
  • Steinmetz solid (solving this takes calculus)

⁵ Three physicists, and ideas that I didn’t try discussing this week:

• Wikipedia
  • ADM formalism
    • ADM energy and mass (Arnowitt-Deser-Misner formalism)
  • Alcubierre drive
  • Causal structure
  • Charles W. Misner
  • Energy density
  • Hamiltonian mechanics
  • Introduction to general relativity
  • Lorentz factor
  • Metric tensor
  • Metric tensor (general relativity)
  • Richard Arnowitt
  • Stanley Deser
  • Warp drive
    • Einstein’s space warp and real-world physics

⁶ Applied physics, an Applied Physics outfit that’s not with Johns Hopkins University, the White-Juday warp field interferometer, and two (?) papers by Miguel Alcubierre:

• Wikipedia
  • Apollo 11
  • Applied physics
  • Harold G. White
    • Alcubierre “warp” drive
  • Johns Hopkins University
  • Miguel Alcubierre (Miguel Alcubierre Moya, theoretical physicist)
  • Theoretical physics
• Applied Physics (appliedphysics.org)
  • About Applied Physics
  • Warp Drive Research
• Johns Hopkins University
  • Johns Hopkins University Applied Physics Laboratory
• “The Inability of the White-Juday Warp Field Interferometer to Spectrally Resolve Spacetime Distortions“
  Jeff Lee, Gerald Cleaver; ; preprint draft (submitted July 29, 2014; updated July 31, 2014) via arXiv, Cornell University
• NASA
  • “Warp Field Mechanics 101”
    Dr. Harold “Sonny” White, NASA Johnson Space Center (2011)
    (from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492_2011024705.pdf (March 18, 2013))
  • “Eagleworks Laboratories: Advanced Propulsion Physics Research”
    Dr. Harold “Sonny” White, Paul March, Nehemiah Williams, William O’Neill; NASA Johnson Space Center (2011)
    (from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf (March 18, 2013))
• “The Warp Drive: Hyper-fast Travel Within General Relativity”
  Miguel Alcubierre; preprint draft (submitted September 5, 2000) published in Classical and Quantum Gravity, IOP Publishing (September 2000) via arXiv, Cornell University
• “LETTER TO THE EDITOR: The warp drive: hyper-fast travel within general relativity”
  Miguel Alcubierre; abstract; Classical and Quantum Gravity, Volume 11, Issue 5, pp. L73-L77 (1994) via ads (astrophysics data system), Harvard

⁷ That March, 2013, cybersecurity mess is almost entirely off the radar now:

• “Nasa hack exposes space agency staff’s data”
  BBC News (December 19, 2018)
• “NASA Takes Down Database After Contractor Arrested”
  Brian Prince, SecurityWeek (March 25, 2013)

⁸ Dark matter and dreamers:

• Wikipedia
  • Dark matter
  • Hermann Oberth
  • Konstantin Tsiolkovsky
  • Robert H. Goddard
  • Tsiolkovsky rocket equation
  • William Moore (mathematician)
• “Contents and Commentary on William Moore’s A Treatise on the Motion of Rockets and as Essay on Naval Gunnery”
  W. Johnson, asdfasdf (Received September 21, 1994) via Stanford University
• “On the Motion of Rockets both in Nonresisting and Resisting Mediums”
  William Moore, Journal of Natural Philosophy, Chemistry & the Arts (1810) via Biodiversity Heritage Library

⁹ Goddard’s March 16, 1926, test flight was the first; but as usual, it’s complicated:

• Wikipedia
  • Liquid-propellant rocket