“‘This,’ said I at length, to the old man — ‘this can be nothing else than the great whirlpool of the Maelström’… The ordinary accounts of this vortex had by no means prepared me for what I saw. That of Jonas Ramus, which is perhaps the most circumstantial of any, cannot impart the faintest conception either of the magnificence, or of the horror of the scene — or of the wild bewildering sense of the novel which confounds the beholder.” So wrote Edgar Allen Poe in 1841 in a short story called “A Descent into The Maelström,” reckoned by some to be an early instance of science fiction. In today’s essay, Adam Crowl explores another kind of whirlpool, armed with the tools of mathematics to take the deepest plunge imaginable, into the maw of a supermassive black hole. Adam’s always fascinating musings can be followed on his Crowlspace site.
by Adam Crowl
The European Southern Observatory’s (ESO) GRAVITY instrument is a beam combiner in the infra-red K-band that operates as a part of the Very Large Telescope Interferometer, combining infra-red light received by four different telescopes, out of the eight operated (four 8.2 metre fixed telescopes and four 1.8 metre movable telescopes).
The latest measurements of the stars orbiting the Milky Way’s Galactic Core Super-Massive Black Hole (SMBH), otherwise known as Sagittarius A* (pronounced as ‘Sagittarius A Star’), by the GRAVITY instrument have determined its mass and distance to new levels of accuracy:
Ro = 8,275 parsecs (+\-) 9.3 parsecs and a mass of (in 106 Msol) 4.297 +\- 0.013.
Image: The galactic centre in infrared. Credit: NASA.
In round figures, that’s 27,000 light-years and 4.3 million Solar masses. The closest that light can approach a Black Hole and still escape is the Event Horizon, which is the spherical boundary at the distance of the Schwarzschild Radius, which is a radius of 2.95325 kilometres per solar mass. Thus 4.3 million solar masses is wrapped in an Event Horizon 12.7 million kilometres in radius. In aeons to come, when the Milky Way and M31 have collided and their black holes have coalesced, the combined Super Massive Black Hole (SMBH) will mass 100 million solar masses with an event horizon almost 300 million kilometres in radius.
Image: From Tales of Mystery and Imagination, by Edgar Allan Poe, with illustrations by Arthur Rackham (1935).
Into the Maelström
Mass-energy, so General Relativity tells us, puts dents into Space-time. Most concentrations of mass-energy, like stars, planets and galaxies, form shallow dents. Black Holes – like the future SMBH – go deeper, forming an inescapable waterfall of space-time inwards to their centres, the edge of which is the Event Horizon.
Light follows the curvature of space-time, traveling the shortest pathways (geodesics). At the Event Horizon the available geodesics all point towards the “middle” of the Black Hole. For particles with rest mass, like atoms, dust and space-ships, geodesics can’t be followed, merely approached, so they follow different pathways just as inexorably towards the centre.
Instead of flying radially inwards towards the future SMBH’s Centre, let’s ponder orbiting it. For most orbital distances from any Black Hole any small mass in orbit will experience nothing different to orbiting around any other large mass. Too close and you’ll experience extreme tidal forces if the black hole is small, so to avoid being torn to shreds when approaching really close a really big Black Hole is needed. The future SMBH massing 100 million solar masses with a Schwarzschild radius of 300 million kilometres has very mild Tidal Forces at the Event Horizon, though potentially significant for things as big as stars and planets.
We have multi-year ‘movies’ of stars orbiting around our SMBH, though none as close as we will explore. Close orbits get measured in multiples of M – which is half the Schwarzschild radius. At a radius of r = 3M space-time is so curved that the geodesics form a circle around the Black Hole. Light can thus orbit indefinitely, building up to potentially extraordinary energy densities if nothing else gets in its way, forming a so-called Photon Sphere. But the centre of the Galaxy is full of dust and gas, so something is always getting in the way. Eventually even photons get so energetic they perturb each other out of the Sphere.
For particles that don’t follow geodesics, merely approximate them, the Innermost Stable Circular Orbit (ISCO) is further out, at r = 6M. Objects here travel at half the speed of light. Other shapes of orbits can dip a bit closer in, down to r = 4M. Deeper in and motion near the Black Hole is no longer “orbital”. You must point away from the Black Hole and apply thrust or in-fall is inevitable.
The equation of orbital motion from the ISCO radius (rI) all the way to the centre was only recently worked out in closed form for rotating and non-rotating (stationary) Black Holes. Previously numerical Relativity methods were used, complicating modelling of Accretion Disks around astrophysical Black Holes. The Equation of Motion of a test particle (i.e. very small mass) around a non-rotating Black Hole, which our future SMBH might approximate, is straightforward:
? is the angular distance traveled, with a range from negative infinity to zero, by convention. I’ve plotted r against ? here:
The Red Circle at r = 3 M is the Photon Sphere and the Yellow Circle at r = 2M is the Schwarzschild Radius aka Event Horizon. In this case the plot starts at r = 5.95M with the test particle circling the Black Hole 6 times before hitting the central point. The proper time experienced by an observer spiralling into the Centre is a bit more complicated. We can parameterise x as follows to make the mathematics easier:
with ? running from an angle ? to 0. Then the Proper-Time ? of the inspiral trajectory is:
The above equation is true for any black-hole, spinning or stationary. For a stationary Black Hole, rI = 6M, so the equation simplifies to:
But what is M? It’s the “geometrised” mass of the Black Hole, which is derived by muliplying the mass by G/c2. Similarly the proper time is in units of “geometrised” time, so it needs to be divided by the speed of light, c, to convert to seconds.
In the case of the fall from r = 5.95M to r = 0, thus ? = (5.95/6) ? (?) to ? = 0, the total time is ? = 1291.14M. In the case of our Galaxy’s SMBH a proper time of M is 493 seconds. So the inspiral time is 176.6 hours and the Event Horizon is reached with 1.32 hours to go.
Surviving the Plunge
Falling into a Black Hole is probably fatal. However, like any fall, it’s not gravity that’ll kill you, but the sudden stop at the end. The final destination is the concentration of mass at the very centre. As the Centre is approached the first derivative of gravitational acceleration with respect to the radial distance vectors – the tidal forces – that will be experienced will become extreme.
Black holes are the pointy end of a spectrum of astrophysical objects. Stars exist due to their dynamic balance between the outward pressure from their fusion energy production and the inward pressure from their self gravity. When fusion energy production ends, the cores of stars begin collapsing, held above the Abyss of gravitational collapse by successive fusion energy reactions, then electron degeneracy pressure from squeezing free electrons too close together (via the Pauli Exclusion Principle), and when that isn’t enough, neutron degeneracy pressure and beyond.
Pressure is a measure of the ‘expansive’ energy packed in a volume. Dimensionally we can see that F / m2 (Pressure) = E / m3 (Energy per unit volume), so that as the mutual gravitational squeeze pushes inwards on a mass of particles which are pushing back against each other thanks to the Pauli Exclusion Principle for fermions (electrons, protons, neutrons etc) that pressure increases and increases, in a feed-back loop. Too much and equilibrium is never achieved. Thanks to Special Relativity we know that energy has mass, so that Pressure adds to the inward squeeze of gravity as particles are squeezed harder together. When the Gravity Squeeze – Push-Back Pressure process self-amplifies and runs away, the mass collapses ‘infinitely’ inwards forming a Singularity. Such a Singularity cuts itself of from the rest of the Universe when it squeezes inwards past the mass’s Schwarzschild Radius:
The resulting Event Horizon defines a Black Hole, by being a ‘surface of no return’ for everything, including light. Nothing escapes from within the Event Horizon. The minimum mass to cause such an inwards collapse and form a Black Hole for a mass of fermions (i.e. the same particles that make Stars, humans and space-ships) in the present day Universe is about 3 solar masses, squished into a volume smaller than 18 kilometres across.
Before we get to that point there are White Dwarfs and Neutron Stars – objects supported against collapse by Electron Degeneracy Pressure and Neutron Degeneracy Pressure, respectively. White Dwarfs are typically composed of carbon and oxygen – the ashes of helium fusion – and have observed masses anywhere between 0.1 and 1.3 Solar masses. Their radius is proportional to the inverse 1/3 power of their mass:
R* is a reference radius. For a cool white dwarf of 1 solar mass, the radius is about 0.8 Earth’s – 5,600 km. A space vehicle falling from infinity, on a flyby very close to such a star’s surface will rush past the lowest point of its orbit at 6,900 km/s, experiencing over 430,000 gee acceleration. In free-fall however it feels only the first derivative of that acceleration:
Which in this example is 0.15 gee per metre of radial stretching directed outwards and inwards along the direction of the radial distance to the white dwarf and a squeezing force half that directed laterally inwards from the sides. Easily resisted by small structures, like bodies and space-ships.
Neutron stars are smaller again – typically 20 km wide for a 1.3 solar mass neutron star. A near surface flyby isn’t recommended, since the tidal forces are thus almost a million times stronger. Close proximity to a magnetic neutron star is probably lethal anyway due to the intense magnetic fields long before the tidal forces rip you to shreds. Heavier neutron stars get smaller – just like white dwarfs – until they totally collapse as a black hole.
Black holes reverse the trend. The Event Horizon gets bigger linearly with their mass and there’s no upper limit to their mass. Our future Galactic SMBH’s Event Horizon will be 295.325 million kilometres in radius, give or take. Substituting the Schwarzschild Radius equation into the Tidal force equation gives us:
So the tidal force at the Event Horizon is 0.1 microgee per metre. The Moon could almost enter the Event Horizon peacefully…
How far into the SMBH can we, as Observers, then fall? If we can brace ourselves against 1,000 gees per metre of squeezing and stretching, then quite a long way…
Which gives a distance of 139,430 kilometres from the centre. In other words 99.953% of the way to the central Singularity.
What wonders might we see? Quantum Gravity is yet to give a clear answer. Traditionally an imploding mass ends in the Singularity, which is a geometrical point. But quantum particles can’t be reduced to a singular point and retain quantum information. A possibility, due to the massively distorted space-time around the collapsing mass, is that ultimately the quantum particles all “bounce” after hitting Planck density and explode back outwards. To external Observers this is seen, in time-dilated fashion, as the slow-leak from the Event Horizon that is Hawking Radiation. Or, if the particles “twist” in a higher dimension, so they bounce as a new Big Bang forming another Universe. This can be seen as an emergence from a White Hole, as White Holes must keep expanding else they collapse into another Black Hole.
None of those options are ‘healthy’ to be around as flesh-and-blood Observer, so presently surviving the plunge is in doubt.
As we conclude, let’s check back in with Edgar Allan Poe, who knew a few things about terrifying plunges himself. In “Descent into the Maelstrom,” he gives us a look into what might be considered a 19th Century conception of a black hole and the journey into its bizarre interior:
“Looking about me upon the wide waste of liquid ebony on which we were thus borne, I perceived that our boat was not the only object in the embrace of the whirl. Both above and below us were visible fragments of vessels, large masses of building timber and trunks of trees, with many smaller articles, such as pieces of house furniture, broken boxes, barrels and staves. I have already described the unnatural curiosity which had taken the place of my original terrors. It appeared to grow upon me as I drew nearer and nearer to my dreadful doom. I now began to watch, with a strange interest, the numerous things that floated in our company. I must have been delirious — for I even sought amusement in speculating upon the relative velocities of their several descents toward the foam below. ‘This fir tree,’ I found myself at one time saying, ‘will certainly be the next thing that takes the awful plunge and disappears,’ — and then I was disappointed to find that the wreck of a Dutch merchant ship overtook it and went down before. At length, after making several guesses of this nature, and being deceived in all — this fact — the fact of my invariable miscalculation — set me upon a train of reflection that made my limbs again tremble, and my heart beat heavily once more.”
Mummery, A. & Balbus, S. “Inspirals from the innermost stable circular orbit of Kerr black holes: Exact solutions and universal radial flow,” Physical Review Letters 129, 161101 (12 October 2022).
Fragione, G. and Loeb, A., “An Upper Limit on the Spin of SgrA* Based on Stellar Orbits in Its Vicinity” (2020) ApJL 901 L32
Moving propulsion technology forward is tough, as witness our difficulties in upgrading the chemical rocket model for deep space flight. But as we’ve often discussed on Centauri Dreams, work continues in areas like beamed propulsion and fusion, even antimatter. Will space drives ever become a possibility? Greg Matloff, who has been surveying propulsion methods for decades, knows that breakthroughs are both disruptive and rare. But can we find ways to increase the odds of discovery? A laboratory created solely to study the physics issues space drives would invoke could make a difference. There is precedent for this, as the author of The Starflight Handbook (Wiley, 1989) and Deep Space Probes (Springer, 2nd. Ed., 2005) makes clear below.
by Greg Matloff
We live in very strange times. The possibility of imminent human contraction (even extinction) is very real. So is the possibility of imminent human expansion.
On one hand, contemporary global civilization faces existential threats from global climate change, potential economic problems caused by widespread application of artificial intelligence, the still-existing possibility of nuclear war, political instability, at many levels, an apparently endless pandemic, etc.
Image: Gregory Matloff (left) being inducted into the International Academy of Astronautics by JPL’s Ed Stone.
One the other hand, humanity seems poised for the long-predicted but oft-delayed breakout into the solar system. United States and Chinese national space programs will compete for lunar resources. Elon Musk’s SpaceX has its sights fixed on establishing human settlements on Mars. Jeff Bezos’ Blue Origin is concentrating on construction of in-space settlements of increasing population and size.
Because of the discovery of a potentially habitable planet circling Proxima Centauri and the possibility of other worlds circling in the habitable zones of Alpha Centauri A and B, one wonders how many decades it will take for an in-space settlement with a mostly closed ecology to begin planning for a change of venue from Sol to Centauri.
Consulting the literature reveals that controlled (or partially controlled) nuclear fusion and the photon sail are today’s leading contenders to propel such a venture. But the literature also reveals that travel times of 500-1,000 years are expected for human-occupied vessels propelled by fusion or radiation pressure.
Before interstellar mission planners finalize their propulsion choice, an ethical question must be addressed. In the science-fiction story “Far Centaurus”, originally published by A, E. van Vogt in 1944, the crew of a 500-year sleeper ship to the Centauri system awakens to learn that they must go through customs at the destination. During their long interstellar transit, a breakthrough had occurred leading to the development of a hyper-fast warp drive.
We simply must evaluate all breakthrough possibilities, no matter how far-fetched they seem, before planning for generation ships. The initial crews of these ships and their descendants must be confident that they will be the first humans to arrive at their destination. Otherwise it is simply not fair to dispatch them into the void.
Recently, I was a guest on Richard Hoagland’s radio show “Beyond Midnight”. Although the discussion included such topics as the James Webb Space Telescope, panpsychism, stellar engineering and ‘Oumuamua, I was particularly intrigued when the topic of space drives came up.
Richard is especially interested in possible ramifications of Bruce E. DePalma’s spinning ball experiment, which has not been investigated in depth. He later sent along a 2014 e-mail released to the public from physics Nobel Prize winner Brian D. Josephson discussing another proposed space-drive candidate, the Nassikas thruster. Professor Josephson is of the opinion that this device is well worth further study, writing this:
The Nassikas thruster apparently produced a thrust, both when immersed in its liquid nitrogen bath, and for a short period while suspended in air, until it warmed to above the superconductor critical temperature, this thrust presenting itself as an oscillating motion of the pendulum biased in a particular direction. If this displacement is due to a new kind of force, this would be an important observation; however, until better controlled experiments are performed it is not possible to exclude conventional mechanisms as the source of the thrust.
It is in this area of controlled experiments that we need to move forward. A little research on the Web revealed that there are a fair number of candidate space drives awaiting consideration. Most of these devices are untested. DARPA, NASA and a few other organizations have applied a small amount of funds in recent years to test a few of them—notably the EMdrive and the Mach Effect Thruster.
Experimental analysis of proposed space drives has not always been done on such a haphazard basis. Chapter 13 of my first co-authored book (E. Mallove and G. Matloff, The Starflight Handbook, Wiley, NY, 1989) discusses a dedicated effort to evaluate these devices. It was coordinated by engineer G. Harry Stine, retired USAF Colonel William O. Davis (who had formerly directed the USAF Office of Scientific Research) and NYU physics professor Serge Korff.
Between 1996 and 2002, NASA operated a Breakthrough Physics Program. Marc G. Millis, who coordinated that effort, has contributed here on Centauri Dreams a discussion of the many hoops a proposed space drive must jump through before it is acknowledged as a true Breakthrough [see Marc Millis: Testing Possible Spacedrives]. These ideas were further examined in the book Marc edited with Eric Davis, Frontiers of Propulsion Science, where many such concepts were subjected to serious scientific scrutiny. When I discussed all this in emails with Marc, he responded:
“The dominant problem is the “lottery ticket” mentality (a DARPA norm), where folks are more interested in supporting a low-cost long-shot, rather than systematic investigations into the relevant unknowns of physics. In the ‘lottery ticket’ approach, interest is cyclical depending if there is someone making a wild claim (usually someone the sponsor knows personally – rather than by inviting concepts from the community). With that hype, funding is secured for ‘cheap and quick’ tests that drag out ambiguously for years (no longer quick, and accumulated costs are no longer cheap). The hype and null tests damage the credibility of the topic and interest wanes until the next hot topic emerges. That is a lousy approach.
“That taint of both the null results and ‘lottery ticket’ mentality is why the physics community ignores such ambitions. I tried to attract the larger physics community by putting the emphasis on the unfinished physics, and made some headway there. When the emphasis is on credibility (and funding available), physicists will indeed pursue such topics and do so rigorously. And they will more quickly drop it again if/when the lottery ticket advocates step up again.”
Marc advocates a strategic approach, which he tried to establish as the preferred norm at NASA BPP, thus identifying the most ‘relevant’ open question in physics, and then getting reliable research done on those topics, thereafter letting these guide future inquiries. He believes that the most relevant open questions in physics deal with the source (unknown) and deeper properties of inertial frames (conjectured). Following those unknowns are the additional unfinished physics of the coupling of the fundamental forces (including neutrino properties).
In light of this pivotal period in space history and the ever-increasing contributions of private individuals and organizations, it seems reasonable to conclude that now is an excellent time to establish a well funded facility to continue the work of the Stine et al. team and the NASA Breakthrough Propulsion Physics program.
I see that Erik Lentz (Göttingen University) has just begun a personal blog, something that may begin to attract attention given that Dr. Lentz has offered up a new paper on faster than light travel. At the moment, the blog is bare-bones, listing only the paper itself (citation below) and an upcoming online talk that may be of interest. Here’s what the Lentz blog has on this:
Upcoming online talk to be given on 18 March 2021 at 3pm Eastern Standard Time for the Science Speaker Series at the Jim and Linda Lee Planetarium: https://youtu.be/6O8ji46VBK0
I checked the URL and found the page with a countdown timer, so I assume the event is publicly accessible. I would imagine it will draw a number of curious scientists and lay-people.
On the subject of faster than light travel, much of the work in the journals has evolved from Miguel Alcubierre’s now well known paper “The Warp Drive: Hyper-fast travel within general relativity,” which presented the idea of a ‘bubble’ of spacetime within which a volume of flat space could exist. In other words, it might be possible to enclose a spacecraft within such a bubble. While there is a physical restriction on objects within spacetime moving faster than the speed of light, spacetime itself is theoretically capable of expansion without limit — this is essentially the notion of ‘inflation’ that drives most current thinking about the earliest moments of the universe.
Alcubierre’s paper ran in May, 1994 in the prestigious journal Classical and Quantum Gravity, a venue whose demanding standards of peer review and acceptance give it high credibility. In other words, papers in this journal rightfully attract attention because of the demanding requirements of publication. I had more or less overlooked the new paper by Dr. Lentz until I realized that it was published here, after which I began to take notice.
This does not mean, of course, that either the Alcubierre ‘warp drive’ concept or the much different ideas of Erik Lentz can ever be engineered, but it does offer a great deal of interest from the standpoint of the mathematics of warped spacetime. After the Alcubierre paper, much of the ongoing work has been involved in exploring how negative energy operates, for ‘negative energy density’ is exotic and vast amounts would be required to form the needed ‘bubble’ of spacetime. The Lentz paper does away with negative energy. I’m hearing it described as an idea more in conformance with conventional physics, though that may also need clarification.
The essential notion put forward by Dr. Lentz is that there are configurations of spacetime curvature that can be explored as ‘solitons,’ which are a solution he deems physically viable, and thus not dependent on negative energy at all. Here we’re already in deep water. A soliton, as I have been learning, is a wave that can retain its shape and move at constant velocity. That such curiosities are within the realm of physical possibility is made clear by the origin of the study of solitons. They actually go back to an observation by British engineer John S. Russell in 1834. In a famous and oft-quoted passage delivered ten years later to the British Association for the Advancement of Science, Russell had this to say about what he called a ‘wave of translation’:
I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped – not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.
Thus was born the study of solitons, which now extends into nuclear physics, optics and other fields, now including exotic propulsion. Notice that what Russell describes is a wave that is stable and can travel. His use of the word ‘translation’ means that this is not a wave made up of the same water that travels the length of the channel he was observing, but rather a wave that moves through the medium. Water is moving but being displaced in the process. We can think of the wave of translation — or at least I’ve seen it referred to this way — as a ‘wave packet’ that can maintain its shape, as it did in Scotland’s Union Canal for Russell.
I turned to Hilborn and Cross’ Chaos and Nonlinear Dynamics (Oxford University Press, 2000) to see solitons described as ‘nonlinear wave phenomena.’ Thus:
A soliton is a spatially localized wave disturbance that can propagate over long distances without changing itsshape. In brief, many nonlinear spatial modes become synchronized to produce a stable localized disturbance.
Solitons turn out to be remarkably stable. A great deal of mathematics has gone on since as solition concepts evolved, all much beyond my pay grade. I looked again at Dr. Lentz’ website to get a notion of what he was proposing in his own words, because I find it hard to make the considerable jump from the early observations of Russell to today’s understanding of solitons. Here’s Lentz with a vest-pocket description of faster than light travel that does not violate Einsteinian relativity:
Hyper-fast (as in faster than light) solitons within modern theories of gravity have been a topic of energetic speculation for the past three decades. One of the most prominent critiques of compact mechanisms of superluminal motion within general relativity is that the geometry must largely be sourced from a form of negative energy density, though there are no such known macroscopic sources in particle physics. I was recently able [to] disprove this position by constructing a new class of hyper-fast soliton solutions within general relativity that are sourced purely from positive energy densities, thus removing the need for exotic negative-energy-density sources. This is made possible through considering hyperbolic relations between components of the space–time metric’s shift vector. Further, these solutions are sourceable by a classical electronic plasma, placing superluminal phenomena into the purview of known physics. This is a very exciting breakthrough that I hope to have more [to] report on soon.
I take this to mean that there are mathematical solutions for spacetime curvature that use solitons as the mode of organization. Alcubierre’s ‘warp bubble’ becomes, in soliton mode, a wave that maintains its shape and moves at constant velocity. The key here, Lentz believes, is that this is a way of altering spacetime geometry without the use of exotic negative energy. Moreover, Lentz’ equations evidently show that tidal forces within the bubble can be minimized. The passage of time inside the soliton can be adjusted to match the time outside the bubble.
Image: Artistic impression of different spacecraft designs considering theoretical shapes of different kinds of “warp bubbles.” Credit: E Lentz.
We would still need enormous amounts of energy, but we are dealing with the kind of energy we understand rather than the far more amorphous ‘negative energy.’ Here’s Lentz again:
“The energy required for this drive travelling 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… Fortunately, several energy-saving mechanisms have been proposed in earlier research that can potentially lower the energy required by nearly 60 orders of magnitude.”
Such energy savings methods would be prodigious indeed and it is to these that Dr. Lentz apparently turns next. The paper is Lentz, “Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory,” Classical and Quantum Gravity Vol. 38, No. 7 (March, 2021). Abstract. We are in very deep mathematical waters here, so all I want to do is point to the paper and urge those interested to take in Dr. Lentz’ talk on the 18th.
Harold “Sonny” White’s investigations into controversial concepts like EMdrive and Alcubierre warp drive physics at Eagleworks Laboratories (located at the Johnson Space Center in Houston) received a good deal of attention in the interstellar community. In a recent email, Dr. White told me that he left NASA in December of 2019 and is now affiliated with the Limitless Space Institute, serving as its Director of Advanced Research and Development. The recently launched LSI is creating a series of initiative grants in support of interstellar research. What follows is the news release LSI has just released.
Limitless Space Institute announces biennial Interstellar Initiative Grants (I2 Grants)
Limitless Space Institute is launching biennial research grants with the goal of providing measurable and consistent support for pursuing interstellar research called Interstellar Initiative Grants. This call for proposals is seeking to support grants that can be categorized as either a tactical grant (?$100k) or a strategic grant (?$250k), with the former focused on research papers and the latter on laboratory testing. The anticipated period of performance for the grants is expected to be ~12-14 months in duration, with a start date by the end of September 2020. It is LSI’s vision that by establishing the Interstellar Initiative Grants, and by conducting these grant awards on a biennial cycle, LSI will help grow and mature the capabilities of the interstellar research community. For more information, see https://www.limitlessspace.org/
Email Contact: firstname.lastname@example.org
Limitless Space Institute is a non-profit organization whose mission is to inspire and educate the next generation to travel beyond our solar system and to research and develop enabling technologies. LSI advances the pursuit of relevant deep space exploration R&D through the following three approaches:
• Internal R&D: pursuing in-house basic research at the Eagleworks Laboratories near Johnson Space Center.
• External R&D: directly funding selected R&D projects through I2 Grants.
• Collaborative R&D: advancing research in collaboration with university partners.
LSI was founded by Dr. Kam Ghaffarian, previously founder of the award-winning contractor Stinger Ghaffarian Technologies and recognized by Ernst & Young as Entrepreneur of the Year. LSI’s president is Brian “BK” Kelly, who served with NASA for 37 years, most recently as Director of Flight Operations, responsible for selecting astronauts and planning and implementing human spaceflight missions. Dr. Harold “Sonny” White leads LSI’s Advanced R&D, bringing decades of research experience in the advanced power and propulsion domain, most recently serving as the NASA Johnson Space Center Engineering Directorate’s Advanced Propulsion Theme Lead.
Image: A Bussard ramjet in flight, as imagined for ESA’s Innovative Technologies from Science Fiction project. Credit: ESA/Manchu.
Avi Loeb’s new foray into the remote future had me thinking of the Soviet physicist Leonid Shkadov, whose 1987 paper “Possibility of Controlling Solar System Motion in the Galaxy” (citation below) discussed how an advanced civilization could get the Sun onto a new trajectory within the galaxy. Why would we want to do this? Shkadov could imagine reasons of planetary defense, a star being moved out of the way of a close encounter with another star, perhaps.
All of this may remind science fiction readers of Robert Metzger’s novel CUSP (Ace, 2005), which sees the Sun driven by a massive propulsive jet. A more recent referent is Gregory Benford and Larry Niven’s novels Bowl of Heaven (Tor, 2012) and ShipStar (2014), in which a star is partially enclosed by a Dyson sphere and used to explore the galaxy. In 1973, Stanley Schmidt would imagine Earth itself being moved to M31 as a way of avoiding an explosion in the core of the Milky Way that threatens all life (Sins of the Fathers, first published as a serial in Analog).
Loeb’s paper mentions technologies for moving stars because several recent proposals involve this kind of ‘cosmic engineering’ to change civilizational outcomes. The accelerated expansion of the universe will, after the universe has aged by a factor of 10, make all stars outside the Local Group of galaxies disappear as they recede. The process continues with continued acceleration. Wait long enough and we fall prey to cosmic winter, and as Loeb writes:
Following the lesson from Aesop’s fable “The Ants and the Grasshopper,” it would be prudent to collect as much fuel as possible before it is too late, for the purpose of keeping us warm in the frigid cosmic winter that awaits us. In addition, it would be beneficial for us to reside in the company of as many alien civilizations as possible with whom we could share technology, for the same reason that animals feel empowered by congregating in large herds.
There are places where we might do this, says Loeb, and I’ll talk about his ideas on them tomorrow. For today, note that in response to his previous papers on the oncoming ‘cosmic isolation,’ Freeman Dyson proposed to Loeb his own project that would move stars, bringing large-scale formations of stars down to a more manageable volume so that they will be bound by their own gravity. Closely spaced, the stellar collection avoids being dissipated in the accelerated expansion of the cosmos. And it turns out that Dan Hooper (University of Chicago) has also been pondering induced stellar motion, using the energy output of stars to cluster large numbers of them into an astronomically tight radius so that their energies can be harvested.
Image: A Shkadov thruster as conceived by the artist Steve Bowers.
Like Dyson and Loeb, Hooper has his eye on the acceleration of cosmic expansion and its consequences. So what kind of ‘stellar engines’ can we envision that could move objects as large as stars? Leonid Shkadov suggested using a star’s radiation pressure. The Shkadov thruster extracts energy from the star by using a vast mirror to take advantage of photon momentum. Let me turn back to an earlier post to reprint a diagram that Duncan Forgan uses in describing a Shkadov thruster. Forgan (University of Edinburgh) points out the difference between these thrusters and Dyson spheres, the latter being spherical and shaped so as to balance gravitational forces on the sphere by way of collecting a maximum amount of stellar energy. But here is the Shkadov thruster as diagrammed by Forgan:
Image: This is Figure 1 from Duncan Forgan’s paper “On the Possibility of Detecting Class A Stellar Engines Using Exoplanet Transit Curves.” Caption: Diagram of a Class A Stellar Engine, or Shkadov thruster. The star is viewed from the pole – the thruster is a spherical arc mirror (solid line), spanning a sector of total angular extent 2?. This produces an imbalance in the radiation pressure force produced by the star, resulting in a net thrust in the direction of the arrow. Credit: Duncan Forgan.
Thus the whole idea of the Shkadov thruster is not balance but imbalance. And Forgan goes on to say this about the idea:
In reality, the re?ected radiation will alter the thermal equilibrium of the star, raising its temperature and producing the above dependence on semi-angle. Increasing ? increases the thrust, as expected, with the maximum thrust being generated at ? = ? radians. However, if the thruster is part of a multi-component megastructure that includes concentric Dyson spheres forming a thermal engine, having a large ? can result in the concentric spheres possessing poorer thermal ef?ciency.
Efficient or not, Shkadov thrusters interest Forgan as a possible SETI detection (Hooper also notes the possibility). Like Dyson spheres, their sheer scale and unusual features could make them visible in a lightcurve, perhaps with the aid of radial velocity follow-ups. Arguing against the idea, though, is the fact that the Shkadov thruster is probably not the technology our hypothetical future civilization would use to move its star (or stars).
I found this out when I wrote Avi Loeb in reaction to his new paper and mentioned the Shkadov idea. Loeb found Dan Hooper’s ideas (in “Life Versus Dark Energy: How An Advanced Civilization Could Resist the Accelerating Expansion of the Universe,” citation below) to be a better solution to the problem. Here is what Loeb told me in our email exchange yesterday:
The use of the momentum associated with the radiation emitted by the star for its propulsion, as envisioned in Shkadov’s thruster, is much less efficient than using the energy associated with same radiation. The radiation momentum equals its energy divided by the speed of light, c. However, the momentum gained by converting this energy to the kinetic energy of a massive object moving at a speed v is larger by a factor of 2(c/v). This is a huge factor of which Dan Hooper is taking advantage to argue that Sun-like stars can reach a percent of the speed light, 0.01c, in a billion years. If he would have used the momentum of the light emitted by the star as in Shkadov’s thruster, then the attainable speed would have been a hundred times smaller, only of order 30 km/s (similar to the speed of chemical rockets), and the journey being contemplated would have not been feasible. During the age of the Universe (10 billion years) one would only be able to traverse a million light years and not leave the Local Group of galaxies. This is not sufficient for gaining more fuel than available within the Local Group of galaxies.
Thus the problem of the Shkadov thruster: By using the momentum of stellar photons, Shkadov loses efficiency. Loeb adds: “One way to improve the efficiency of Shkadov’s thruster (by employing the energy and not the momentum of the star’s radiation) is to harvest the energy from the star through a Dyson sphere and then use it to ablate its surface on one side, generating a rocket effect.” This seems to be what Dan Hooper has in mind in his paper. The civilization in question would harvest the energy of stars through Dyson spheres that, quoting Hooper, “…use the collected energy to propel the captured stars, providing new and potentially distinctive signatures of an advanced civilization in this stage of expansion and stellar collection.”
Hooper has a SETI prospect in mind, while also thinking about collecting sources of energy, maximizing its amount in the form of starlight by a factor of several thousand. It is this prospect that interests Loeb. His paper makes the case that we already have massive reservoirs of fuel in the visible universe in the form of galactic clusters, each containing the equivalent of 1000 Milky Ways. Perhaps, then, we need no star-moving and collection project a la Hooper or Dyson, but rather need to think about reaching a galactic cluster for our fuel. Given the magnitude of that challenge, whether or not we take our home star along is inconsequential.
The speculative buzz I get from this is science fictional indeed. The nearest cluster is Virgo, whose center is some 50 million light years away, with the Coma cluster six times farther still. Thinking in terms of a civilization that could cross such gulfs takes us into Olaf Stapledon territory, a region of spacetime with which I share Loeb’s obvious fascination. I’m running out of time today, but want to look deeper into this with the help of Loeb’s paper tomorrow. I’ll also have more thoughts on ‘stellar engines’ and their origins.
Avi Loeb’s new paper is “Securing Fuel for Our Frigid Cosmic Future” (preprint). Leonid Shkadov’s paper on the Shkadov thruster is “Possibility of controlling solar system motion in the galaxy,” 38th Congress of IAF,” October 10-17, 1987, Brighton, UK, paper IAA-87-613. The Forgan paper is “On the Possibility of Detecting Class A Stellar Engines Using Exoplanet Transit Curves,” accepted at the Journal of the British Interplanetary Society (preprint). The Hooper paper is “Life Versus Dark Energy: How An Advanced Civilization Could Resist the Accelerating Expansion of the Universe” (2018). Preprint.
I always look at the NASA Innovative Advanced Concepts (NIAC) awards with interest as well as a bit of nostalgia. When I began researching the book that would become Centauri Dreams, NIAC was an early incentive. Then known as the NASA Institute for Advanced Concepts, it was under the direction of Robert Cassanova (this was back around 2002), and its archive of funded studies was a treasure house of deep space ideas, from antimatter extraction in planetary magnetic fields to exoplanet imaging through starshades. I spent days going through any number of reports and interviewed many NIAC study authors.
You can still see the NIAC reports from that era on the older site (go to NIAC Funded Studies). The current NIAC site makes the point that the program looks for “non-traditional sources of innovation that study technically credible, advanced concepts that could one day ‘change the possible’ in aerospace.” And it’s here that we get the 2017 Phase 1 proposals, a $125,000 award for a nine month period that can result in a two-year Phase II follow-up.
Laser-Fed Ion Drive for Interstellar Precursor
2017 proposals with specifically interstellar intent include one from JPL’s John Brophy, who describes what he calls “A Breakthrough Propulsion Architecture for Interstellar Precursor Missions.” Brophy is looking for a way to deliver a high spacecraft velocity change (delta-V) without using much propellant. He envisions a lithium-fueled ion thruster with a specific impulse of 58,000 seconds (compare this with the Dawn spacecraft’s 3,000 seconds).
How to achieve this? By use of a 10-km orbital laser array that allows his craft to operate far beyond the point where sunlight loses its useful effect, the array feeding a lightweight, photovoltaic array aboard the spacecraft that can produce the electric power to drive the thrusters. Brophy believes laser power in this configuration can be converted to electric power at an efficiency of 70 percent, to produce an output voltage of 12 kV. The lithium fueled system would be capable of a 12-year flight-time to 500 AU, close to the point where gravitational lensing begins to get interesting. Time to Pluto: 3.6 years, and Jupiter in a single year.
So much depends upon that laser array, a ground-based version of which is under active study by the Breakthrough Starshot effort. The problems of implementing such an array are daunting, but its uses if ever built are so game-changing that the investigation continues. Breakthrough Starshot itself works with a 30-year horizon, so we are not talking about near-term implementation, but rather sketching out concepts a laser array could make feasible.
Image: Breakthrough Propulsion Architecture for Interstellar Precursor Missions
Credit: John Brophy.
Counting on Ernst Mach
Like Brophy’s proposal, Heidi Fearn’s “Mach Effects for In Space Propulsion: Interstellar Mission” is a Phase 1 initiative, an interesting entry because it shows NIAC beginning to open to the kind of breakthrough propulsion concepts NASA once investigated through its Breakthrough Propulsion Physics project (led by Tau Zero founder Marc Millis). In this case, the work goes toward a so-called Mach Effect Thruster (MET). Mach effects are transient variations in the rest masses of objects as predicted by standard physics where Mach’s principle applies. Proponents believe they offer the possibility of producing thrust without the ejection of propellant, as discussed in James Woodward’s Making Starships and Stargates: The Science of Interstellar Transport and Absurdly Benign Wormholes (Springer-Verlag, 2012).
What Fearn proposes is to investigate such thrusters by continuing the development of laboratory-scale devices while designing and developing power supply and electrical systems that will determine the efficiency of the Mach Effect Thruster. The analytical task is to improve theoretical thrust predictions and build a reliable model of the device. At the theoretical level, this team is definitely talking deep space, with part of the proposal being to:
Predict maximum thrust achievable by one device and how large an array of thrusters would be required to send a probe, of size 1.5m diameter by 3m, of total mass 1245 Kg including a modest 400 Kg of payload, a distance of 8 light years (ly) away.
Image: Mach Effects for In Space Propulsion: Interstellar Mission. Credit: Heidi Fearn.
Can such a device work? Remember, we are in the realm of advanced concepts, where the technology is at the TRL 1 level, but the benefits of working with a thruster that does not expel fuel mass could make high velocities possible, enough of an incentive to pursue these early steps. Mach’s principle relates the motion of the farthest objects in the universe to the local inertial frame or, as Hawking has it, “Local physical laws are determined by the large-scale structure of the universe.” The principle is vague enough that Hermann Bondi and Joseph Samuel have compiled eleven different variations on it, all of which could be called Machian.
Gravitational Lensing and Exoplanet Imaging
JPL’s Slava Turyshev is behind a Phase 1 study called “Direct Multipixel Imaging and Spectroscopy of an exoplanet with a Solar Gravity Lens Mission,” a study focusing on a mission to exploit the Sun’s gravitational lens, where (at 550 AU and beyond) the Sun’s gravity has bent the light of objects directly behind it to allow powerful lensing effects.
Long-time Centauri Dreams readers will know that the Italian physicist Claudio Maccone has championed a gravitational lens mission called FOCAL for many years, proposing it to the European Space Agency and writing numerous papers as well as two books on the topic (there is much available in the archives here about this concept). The definitive book, Deep Space Flight and Communications: Exploiting the Sun as a Gravitational Lens (Springer, 2009) lays out the principles of such lensing, the history of its study, and potential solutions to the many imaging issues raised by a space mission. Maccone has discussed lensing as one solution to the communications challenges of Breakthrough Starshot.
What Turyshev is proposing is to study not the means of getting to 550 AU and beyond, but the question of spacecraft operations at such distances. From the proposal description:
Specifically, we propose to study I) how a space mission to the focal region of the SGL (Solar Gravitational Lens) may be used to obtain high-resolution direct imaging and spectroscopy of an exoplanet by detecting, tracking, and studying the Einstein’s ring around the Sun, and II) how such information could be used to unambiguously detect and study life on another planet.
Image: Direct Multipixel Imaging and Spectroscopy of an exoplanet with a Solar Gravity Lens Mission. Credit: Slava Turyshev.
Other proposals of interest are “Pluto Hop, Skip and Jump Global,” from Benjamin Goldman (Global Aerospace Corporation), an innovative study of a Pluto lander with a novel approach to landing and in situ science; “Gradient Field Imploding Liner Fusion Propulsion System” from Michael LaPointe (NASA MSFC), exploring magneto-inertial fusion in a new configuration that could lend itself to in-space propulsion; and “Fusion-Enabled Pluto Orbiter and Lander,” from Stephanie Thomas (Princeton Satellite Systems, Inc.), a Direct Fusion Drive concept based on work under development at the Princeton Plasma Physics Laboratory, and its application in a Pluto orbiter with lander (this one is a Phase II study).
The full list of 2017 Phase I and Phase II selections is here, including Nan Yu’s interesting take at JPL on possible dark energy interactions with a ‘Solar System laboratory.’ Have a look at these and ask yourself which we may still be talking about a decade hence. When I look back to the NIAC studies I examined in 2002 and later, I find many ideas that we wound up discussing at length here on the site, and I wouldn’t be surprised if several of the new selections move on to Phase II status and a great deal of future scrutiny. Which ones will they be?